The document describes a chess match between a Home team and Away team played across 4 boards. On each board, the probability of the Home team winning is 0.2, drawing is 0.6, and losing is 0.2. The results are recorded as a string of W, D, L representing the outcome on each board. There are 3 possible outcomes on each board, so there are 3^4 = 81 possible result recordings.
12X1 T09 06 probability and counting techniques (2010)Nigel Simmons
- A chess match involves 4 games played between the Home and Away teams on boards 1-4
- The probability of the Home team winning, drawing, or losing each game is 0.2, 0.6, and 0.2 respectively
- The results are recorded by listing the outcome (win, draw, loss) of each game for the Home team
- There are 81 possible different recordings as there are 3 possible outcomes for each of the 4 games
- The probability of the recording "WDLD" is 0.2 × 0.6 × 0.2 × 0.6 = 0.0144
The document provides solutions to probability questions involving throwing ninja stars.
For the first question, the probability of at least two stars being black if three stars are thrown without replacement is calculated to be 40%.
The second question calculates the probability of the third star being red as 25%.
The third question considers a scenario where the colors are replaced after each throw, and calculates the probability of the second star being blue as 32%.
11X1 T05 04 probability & counting techniques (2011)Nigel Simmons
- A chess match between a Home and Away team is played across 4 boards
- The probability of the Home team winning, drawing, or losing on each board is given
- The results are recorded as a string of W, D, L indicating the outcome on each board
- There are 81 possible result recordings as there are 3 possible outcomes on each of the 4 boards
- The probability of the result "WDLD" is calculated as the product of the probabilities of each individual outcome
A combination is a set of objects where the order the objects are arranged is not important. If the order is not important, arrangements like "AB" and "BA" are considered the same combination. The number of combinations of choosing k objects from n total unique objects is calculated as nCk, read as "n choose k". This counts the number of unique groups that can be formed without regard to order.
The document discusses permutations and arrangements of objects where some objects are the same. It provides examples of calculating the number of arrangements of letters in words where some letters are duplicated. The key points are:
- To calculate the number of arrangements of n objects where x objects are the same, the formula is n! / x!.
- This accounts for the ways of arranging the n objects and dividing by the ways of arranging the duplicated objects.
- Examples provided calculate the number of arrangements of letters in words like 'CONNAUGHTON' and 'ALGEBRAIC' where some letters are duplicated.
12X1 T09 07 arrangements in a circle (2010)Nigel Simmons
The document discusses the difference between arranging objects in a line versus in a circle. When objects are arranged in a circle, there is no defined start or end point. Therefore, the number of arrangements is equal to the factorial of the number of objects divided by the number of objects. This is because any object can be chosen as the starting point, but those arrangements are considered identical in a circular arrangement. The document provides examples of calculating the number of arrangements of people seated around a circular table.
The document discusses tree diagrams and their uses in probability calculations. It provides examples of using tree diagrams to calculate the probability of events involving draws from a hat containing boy and girl names. It explains that for "and" events, the probabilities are multiplied, while for "or" events they are added. The document also works through examples of using tree diagrams to calculate the probability of winning prizes in a raffle where tickets and prizes are given. It specifically calculates the probability of winning exactly one prize when buying 5 tickets for a raffle with 30 total tickets and 2 prizes.
The document discusses the basic counting principle and provides examples of applying it to situations involving rolling dice and mice in a maze. It states that if one event can occur in m ways and a subsequent event can occur in n ways, the total number of ways both events can occur is mn. For rolling 3 dice, the number of possibilities is 6x6x6 = 216. The probability of all 3 dice showing the same number is 6/216 = 1/36. For mice in a maze with 5 exits, the probability of all 4 mice exiting through the same door is 1/125, while the probability of mice A, B, C using the same exit and mouse D using a different exit is 4/5x1
12X1 T09 06 probability and counting techniques (2010)Nigel Simmons
- A chess match involves 4 games played between the Home and Away teams on boards 1-4
- The probability of the Home team winning, drawing, or losing each game is 0.2, 0.6, and 0.2 respectively
- The results are recorded by listing the outcome (win, draw, loss) of each game for the Home team
- There are 81 possible different recordings as there are 3 possible outcomes for each of the 4 games
- The probability of the recording "WDLD" is 0.2 × 0.6 × 0.2 × 0.6 = 0.0144
The document provides solutions to probability questions involving throwing ninja stars.
For the first question, the probability of at least two stars being black if three stars are thrown without replacement is calculated to be 40%.
The second question calculates the probability of the third star being red as 25%.
The third question considers a scenario where the colors are replaced after each throw, and calculates the probability of the second star being blue as 32%.
11X1 T05 04 probability & counting techniques (2011)Nigel Simmons
- A chess match between a Home and Away team is played across 4 boards
- The probability of the Home team winning, drawing, or losing on each board is given
- The results are recorded as a string of W, D, L indicating the outcome on each board
- There are 81 possible result recordings as there are 3 possible outcomes on each of the 4 boards
- The probability of the result "WDLD" is calculated as the product of the probabilities of each individual outcome
A combination is a set of objects where the order the objects are arranged is not important. If the order is not important, arrangements like "AB" and "BA" are considered the same combination. The number of combinations of choosing k objects from n total unique objects is calculated as nCk, read as "n choose k". This counts the number of unique groups that can be formed without regard to order.
The document discusses permutations and arrangements of objects where some objects are the same. It provides examples of calculating the number of arrangements of letters in words where some letters are duplicated. The key points are:
- To calculate the number of arrangements of n objects where x objects are the same, the formula is n! / x!.
- This accounts for the ways of arranging the n objects and dividing by the ways of arranging the duplicated objects.
- Examples provided calculate the number of arrangements of letters in words like 'CONNAUGHTON' and 'ALGEBRAIC' where some letters are duplicated.
12X1 T09 07 arrangements in a circle (2010)Nigel Simmons
The document discusses the difference between arranging objects in a line versus in a circle. When objects are arranged in a circle, there is no defined start or end point. Therefore, the number of arrangements is equal to the factorial of the number of objects divided by the number of objects. This is because any object can be chosen as the starting point, but those arrangements are considered identical in a circular arrangement. The document provides examples of calculating the number of arrangements of people seated around a circular table.
The document discusses tree diagrams and their uses in probability calculations. It provides examples of using tree diagrams to calculate the probability of events involving draws from a hat containing boy and girl names. It explains that for "and" events, the probabilities are multiplied, while for "or" events they are added. The document also works through examples of using tree diagrams to calculate the probability of winning prizes in a raffle where tickets and prizes are given. It specifically calculates the probability of winning exactly one prize when buying 5 tickets for a raffle with 30 total tickets and 2 prizes.
The document discusses the basic counting principle and provides examples of applying it to situations involving rolling dice and mice in a maze. It states that if one event can occur in m ways and a subsequent event can occur in n ways, the total number of ways both events can occur is mn. For rolling 3 dice, the number of possibilities is 6x6x6 = 216. The probability of all 3 dice showing the same number is 6/216 = 1/36. For mice in a maze with 5 exits, the probability of all 4 mice exiting through the same door is 1/125, while the probability of mice A, B, C using the same exit and mouse D using a different exit is 4/5x1
11 x1 t05 04 probability & counting techniques (2012)Nigel Simmons
- A chess match between a Home and Away team is played across 4 boards
- The probability of the Home team winning, drawing, or losing on each board is given
- The results are recorded as a string using W, D, L to indicate the outcome on each board
- There are 81 possible different result recordings as there are 3 possible outcomes on each of the 4 boards
- The probability of the result "WDLD" is calculated as 0.2 × 0.6 × 0.2 × 0.6 = 0.0144
This document discusses the differences between arranging objects in a line versus arranging them in a circle. When objects are arranged in a line, there is a definite start and end point, so the first object can be placed in any of n positions. However, when objects are arranged in a circle, there is no definite start or end, so the number of arrangements for the first object is always 1, since its position defines where the circle begins. As a result, the total number of arrangements of n objects in a circle is n!, while the number in a line is n*(n-1)*(n-2)...1. Examples are provided to illustrate calculating arrangements of objects in circles.
11 x1 t05 04 probability & counting techniques (2013)Nigel Simmons
The document describes a chess match between a Home team and Away team played across 4 boards. On each board, the probability of the Home team winning is 0.2, drawing is 0.6, and losing is 0.2. The results are recorded as a string of W, D, L representing the outcome on each board. There are 3 possible outcomes on each board, so there are 3^4 = 81 possible result recordings.
12X1 T09 01 definitions and theory (2010)Nigel Simmons
The document defines key probability terms like probability, sample space, equally likely events, mutually exclusive events, and non-mutually exclusive events. It also provides the formula for calculating probability as the number of favorable outcomes divided by the total number of possible outcomes. As an example, it calculates the probability of throwing a total of 3 or 7 when rolling a pair of dice.
The document defines various terms related to circle geometry, including radius, diameter, chord, secant, tangent, arc, sector, segment, and more. It also presents several theorems regarding chords and arcs, such as a perpendicular from the circle's center bisects a chord, equal chords subtend equal angles at the center, and more. Diagrams with proofs are provided.
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
This document discusses independent and dependent probability through examples involving drawing marbles from a bag. It explains that if the outcome of one event affects the outcome of another event, the events are dependent, but if the outcomes do not affect each other, the events are independent. Several examples are provided of experiments involving dependent and independent events.
Here is the tree diagram and sample space for flipping a coin and rolling a die:
H
T
1
2
3
4
5
6
1
2
3
4
5
6
Sample space: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
There are 12 outcomes in the sample space.
The document discusses permutations, combinations, and probability. It provides examples and formulas for calculating the number of permutations of objects taken a certain number at a time. It also discusses combinations and provides examples. The document then provides several word problems involving permutations, combinations, and calculating probabilities of events occurring.
The document provides solutions to probability questions involving throwing ninja stars.
For the first question, the probability of at least two stars being black if three stars are thrown without replacement is calculated to be 40%.
The second question calculates the probability of the third star being red as 25%.
The third question considers a scenario where the colors are replaced after each throw, and calculates the probability of the second star being blue as 32%.
The document discusses probability and provides examples and solutions. It defines probability as the number of favorable outcomes divided by the total number of possible outcomes. It gives examples of calculating probabilities of events such as choosing balls of different colors from a bag. It also discusses combined events and finding probabilities of "or" and "and" events.
The document contains 20 math assignment questions covering various topics:
- Solving systems of linear equations using substitution, elimination, and cross multiplication methods
- Solving pairs of linear equations and finding values of variables
- Finding values that satisfy or cause certain properties in systems of linear equations
- Solving quadratic and cubic polynomial equations
- Finding quadratic polynomials based on properties of their zeros
- Solving geometry problems using concepts like midpoints, centroids, and collinearity
- Calculating probabilities of outcomes in experiments involving balls, cards, dice, and coins
- Solving quadratic equations by finding discriminants and values that produce equal roots
- Solving word problems involving rates, speeds, mixtures, and geometric concepts
I am Josh U. I am a Probability Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from St. Edward’s University, USA.
I have been helping students with their homework for the past 5 years. I solve assignments related to Probability. Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Probability Assignments.
Worksheet works theoretical_probability_1agussadiya
The document contains 8 probability word problems involving rolling dice, picking marbles from jars, drawing cards, and guessing numbers. The problems calculate probabilities of outcomes such as rolling a multiple of 3 on a 19-sided die, picking a red or green marble from a jar with different colored marbles, drawing the two of clubs from a standard card deck, guessing an even number between 7 and 14, drawing a letter after L in the alphabet, rolling a 3 or 2 on an 8-sided die, and picking a marble that is neither red nor blue from a jar with different colored marbles. The document also provides an answer key with the calculation and percentage probability for each problem.
The document discusses different methods for factorising expressions:
1) Looking for a common factor and dividing it out of all terms
2) Using the difference of two squares formula (a2 - b2 = (a - b)(a + b))
3) Factorising quadratic trinomials into two binomial factors by identifying the values that multiply to give the constant term and sum to give the coefficient of the linear term.
The document provides information on index laws and the meaning of indices in algebra:
- Index laws state that am × an = am+n, am ÷ an = am-n, and (am)n = amn. Exponents can be added or subtracted when multiplying or dividing terms with the same base.
- Positive exponents indicate a term is raised to a power. Negative exponents indicate a root is being taken. Terms with exponents are evaluated from left to right.
- Examples demonstrate how to simplify expressions using index laws and interpret different types of indices.
12 x1 t01 03 integrating derivative on function (2013)Nigel Simmons
The document discusses integrating derivatives of functions. It states that the integral of the derivative of a function f(x) is equal to the natural log of f(x) plus a constant. It then provides examples of integrating several derivatives: (i) ∫(1/(7-3x)) dx = -1/3 log(7-3x) + c, (ii) ∫(1/(8x+5)) dx = 1/8 log(8x+5) + c, and (iii) ∫(x5/(x-2)) dx = 1/6 log(x6-2) + c. It also discusses techniques for integrating fractions by polynomial long division and finds
11 x1 t05 04 probability & counting techniques (2012)Nigel Simmons
- A chess match between a Home and Away team is played across 4 boards
- The probability of the Home team winning, drawing, or losing on each board is given
- The results are recorded as a string using W, D, L to indicate the outcome on each board
- There are 81 possible different result recordings as there are 3 possible outcomes on each of the 4 boards
- The probability of the result "WDLD" is calculated as 0.2 × 0.6 × 0.2 × 0.6 = 0.0144
This document discusses the differences between arranging objects in a line versus arranging them in a circle. When objects are arranged in a line, there is a definite start and end point, so the first object can be placed in any of n positions. However, when objects are arranged in a circle, there is no definite start or end, so the number of arrangements for the first object is always 1, since its position defines where the circle begins. As a result, the total number of arrangements of n objects in a circle is n!, while the number in a line is n*(n-1)*(n-2)...1. Examples are provided to illustrate calculating arrangements of objects in circles.
11 x1 t05 04 probability & counting techniques (2013)Nigel Simmons
The document describes a chess match between a Home team and Away team played across 4 boards. On each board, the probability of the Home team winning is 0.2, drawing is 0.6, and losing is 0.2. The results are recorded as a string of W, D, L representing the outcome on each board. There are 3 possible outcomes on each board, so there are 3^4 = 81 possible result recordings.
12X1 T09 01 definitions and theory (2010)Nigel Simmons
The document defines key probability terms like probability, sample space, equally likely events, mutually exclusive events, and non-mutually exclusive events. It also provides the formula for calculating probability as the number of favorable outcomes divided by the total number of possible outcomes. As an example, it calculates the probability of throwing a total of 3 or 7 when rolling a pair of dice.
The document defines various terms related to circle geometry, including radius, diameter, chord, secant, tangent, arc, sector, segment, and more. It also presents several theorems regarding chords and arcs, such as a perpendicular from the circle's center bisects a chord, equal chords subtend equal angles at the center, and more. Diagrams with proofs are provided.
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
This document discusses independent and dependent probability through examples involving drawing marbles from a bag. It explains that if the outcome of one event affects the outcome of another event, the events are dependent, but if the outcomes do not affect each other, the events are independent. Several examples are provided of experiments involving dependent and independent events.
Here is the tree diagram and sample space for flipping a coin and rolling a die:
H
T
1
2
3
4
5
6
1
2
3
4
5
6
Sample space: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
There are 12 outcomes in the sample space.
The document discusses permutations, combinations, and probability. It provides examples and formulas for calculating the number of permutations of objects taken a certain number at a time. It also discusses combinations and provides examples. The document then provides several word problems involving permutations, combinations, and calculating probabilities of events occurring.
The document provides solutions to probability questions involving throwing ninja stars.
For the first question, the probability of at least two stars being black if three stars are thrown without replacement is calculated to be 40%.
The second question calculates the probability of the third star being red as 25%.
The third question considers a scenario where the colors are replaced after each throw, and calculates the probability of the second star being blue as 32%.
The document discusses probability and provides examples and solutions. It defines probability as the number of favorable outcomes divided by the total number of possible outcomes. It gives examples of calculating probabilities of events such as choosing balls of different colors from a bag. It also discusses combined events and finding probabilities of "or" and "and" events.
The document contains 20 math assignment questions covering various topics:
- Solving systems of linear equations using substitution, elimination, and cross multiplication methods
- Solving pairs of linear equations and finding values of variables
- Finding values that satisfy or cause certain properties in systems of linear equations
- Solving quadratic and cubic polynomial equations
- Finding quadratic polynomials based on properties of their zeros
- Solving geometry problems using concepts like midpoints, centroids, and collinearity
- Calculating probabilities of outcomes in experiments involving balls, cards, dice, and coins
- Solving quadratic equations by finding discriminants and values that produce equal roots
- Solving word problems involving rates, speeds, mixtures, and geometric concepts
I am Josh U. I am a Probability Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from St. Edward’s University, USA.
I have been helping students with their homework for the past 5 years. I solve assignments related to Probability. Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Probability Assignments.
Worksheet works theoretical_probability_1agussadiya
The document contains 8 probability word problems involving rolling dice, picking marbles from jars, drawing cards, and guessing numbers. The problems calculate probabilities of outcomes such as rolling a multiple of 3 on a 19-sided die, picking a red or green marble from a jar with different colored marbles, drawing the two of clubs from a standard card deck, guessing an even number between 7 and 14, drawing a letter after L in the alphabet, rolling a 3 or 2 on an 8-sided die, and picking a marble that is neither red nor blue from a jar with different colored marbles. The document also provides an answer key with the calculation and percentage probability for each problem.
Similar to 11X1 T06 04 probability and counting techniques (2010) (9)
The document discusses different methods for factorising expressions:
1) Looking for a common factor and dividing it out of all terms
2) Using the difference of two squares formula (a2 - b2 = (a - b)(a + b))
3) Factorising quadratic trinomials into two binomial factors by identifying the values that multiply to give the constant term and sum to give the coefficient of the linear term.
The document provides information on index laws and the meaning of indices in algebra:
- Index laws state that am × an = am+n, am ÷ an = am-n, and (am)n = amn. Exponents can be added or subtracted when multiplying or dividing terms with the same base.
- Positive exponents indicate a term is raised to a power. Negative exponents indicate a root is being taken. Terms with exponents are evaluated from left to right.
- Examples demonstrate how to simplify expressions using index laws and interpret different types of indices.
12 x1 t01 03 integrating derivative on function (2013)Nigel Simmons
The document discusses integrating derivatives of functions. It states that the integral of the derivative of a function f(x) is equal to the natural log of f(x) plus a constant. It then provides examples of integrating several derivatives: (i) ∫(1/(7-3x)) dx = -1/3 log(7-3x) + c, (ii) ∫(1/(8x+5)) dx = 1/8 log(8x+5) + c, and (iii) ∫(x5/(x-2)) dx = 1/6 log(x6-2) + c. It also discusses techniques for integrating fractions by polynomial long division and finds
The document discusses logarithms and their properties. Logarithms are defined as the inverse of exponentials. If y = ax, then x = loga y. The natural logarithm is log base e, written as ln. Properties of logarithms include: loga m + loga n = loga mn; loga m - loga n = loga(m/n); loga mn = n loga m; loga 1 = 0; loga a = 1. Examples of evaluating logarithmic expressions are provided.
The document discusses relationships between the coefficients and roots of polynomials. It states that for a polynomial P(x) = axn + bxn-1 + cxn-2 + ..., the sum of the roots equals -b/a, the sum of the roots taken two at a time equals c/a, and so on for higher order terms. It also provides examples of using these relationships to find the sums of roots for a given polynomial.
P
4
3
2
The document discusses properties of polynomials with multiple roots. It first proves that if a polynomial P(x) has a root x = a of multiplicity m, then the derivative of P(x), P'(x), will have a root x = a of multiplicity m-1. It then provides an example of solving a cubic equation given it has a double root. Finally, it examines a quartic polynomial and shows that its root α cannot be 0, 1, or -1, and that 1/
The document discusses factorizing complex expressions. The main points are:
- If a polynomial's coefficients are real, its roots will appear in complex conjugate pairs.
- Any polynomial of degree n can be factorized into a mixture of quadratic and linear factors over real numbers, or into n linear factors over complex numbers.
- Odd degree polynomials must have at least one real root.
- Examples of factorizing polynomials over both real and complex numbers are provided.
The document describes the Trapezoidal Rule for approximating the area under a curve between two points. It shows that the area A is estimated by dividing the region into trapezoids with height equal to the function values at the interval endpoints and bases equal to the intervals. In general, the area is approximated as the sum of the areas of each trapezoid, which is equal to the average of the endpoint function values multiplied by the interval length.
The document discusses methods for calculating the volumes of solids of revolution. It provides formulas for finding volumes when an area is revolved around either the x-axis or y-axis. Examples are given for finding volumes of common solids like cones, spheres, and others. Steps are shown for using the formulas to calculate volumes based on given functions and limits of revolution.
The document discusses different methods for calculating the area under a curve or between curves.
(1) The area below the x-axis is given by the integral of the function between the bounds, which can be positive or negative depending on whether the area is above or below the x-axis.
(2) To calculate the area on the y-axis, the function is solved for x in terms of y, then the bounds are substituted into the integral of this new function with respect to y.
(3) The area between two curves is calculated by taking the integral of the upper curve minus the integral of the lower curve, both between the same bounds on the x-axis.
The document discusses 8 properties of definite integrals:
1) Integrating polynomials results in a fraction.
2) Constants can be factored out of integrals.
3) Integrals of sums are equal to the sum of integrals.
4) Splitting an integral range results in the sum of the integrals.
5) Integrals of positive functions over a range are positive, and negative if the function is negative.
6) Integrals can be compared based on the relative values of the integrands.
7) Changing the limits of integration flips the sign of the integral.
8) Integrals of odd functions over a symmetric range are zero, and integrals of even functions are twice the integral over
0
The document discusses the relationship between integration and calculating the area under a curve. It shows that the area under a curve from x=a to x=b can be calculated as the integral from a to b of the function f(x) dx. This is equal to the antiderivative F(x) evaluated from b to a. The area under a curve can also be estimated using rectangles, and as the width of the rectangles approaches 0, the estimate becomes the exact area. The derivative of the area function A(x) gives the equation of the curve f(x). Examples are given to calculate the exact area under curves.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
🔥🔥🔥🔥🔥🔥🔥🔥🔥
إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
How to Setup Default Value for a Field in Odoo 17Celine George
In Odoo, we can set a default value for a field during the creation of a record for a model. We have many methods in odoo for setting a default value to the field.
How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
11X1 T06 04 probability and counting techniques (2010)
1. Probability & Counting
Techniques
2007 Extension 1 HSC Q5b)
Mr and Mrs Roberts and their four children go to the theatre. They are
randomly allocated six adjacent seats in a single row.
What is the probability that the four children are allocated seats next to
each other?
2. Probability & Counting
Techniques
2007 Extension 1 HSC Q5b)
Mr and Mrs Roberts and their four children go to the theatre. They are
randomly allocated six adjacent seats in a single row.
What is the probability that the four children are allocated seats next to
each other?
3!4!
P(children sit next to each other)
6!
3. Probability & Counting
Techniques
2007 Extension 1 HSC Q5b)
Mr and Mrs Roberts and their four children go to the theatre. They are
randomly allocated six adjacent seats in a single row.
What is the probability that the four children are allocated seats next to
each other?
3!4!
P(children sit next to each other)
6!
ways of arranging 6 people
4. Probability & Counting
Techniques
2007 Extension 1 HSC Q5b)
Mr and Mrs Roberts and their four children go to the theatre. They are
randomly allocated six adjacent seats in a single row.
What is the probability that the four children are allocated seats next to
each other?
ways of arranging 3 objects
i.e 2 adults + 1 group of 4 children
3!4!
P(children sit next to each other)
6!
ways of arranging 6 people
5. Probability & Counting
Techniques
2007 Extension 1 HSC Q5b)
Mr and Mrs Roberts and their four children go to the theatre. They are
randomly allocated six adjacent seats in a single row.
What is the probability that the four children are allocated seats next to
each other?
ways of arranging 3 objects
i.e 2 adults + 1 group of 4 children ways of arranging 4 children
3!4!
P(children sit next to each other)
6!
ways of arranging 6 people
6. Probability & Counting
Techniques
2007 Extension 1 HSC Q5b)
Mr and Mrs Roberts and their four children go to the theatre. They are
randomly allocated six adjacent seats in a single row.
What is the probability that the four children are allocated seats next to
each other?
ways of arranging 3 objects
i.e 2 adults + 1 group of 4 children ways of arranging 4 children
3!4!
P(children sit next to each other)
6!
ways of arranging 6 people
1
5
7. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
8. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
12
C3 12C3
P(3 red) 24
C6
9. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
12
C3 12C3
P(3 red) 24
C6
0.3595
0.36 (to 2 dp)
10. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
12
C3 12C3
P(3 red) 24
C6
0.3595
0.36 (to 2 dp)
(ii) Hence, or otherwise, calculate the probability that more than three
of the selected marbles are red. Give your answer correct to two
decimal places.
11. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
12
C3 12C3
P(3 red) 24
C6
0.3595
0.36 (to 2 dp)
(ii) Hence, or otherwise, calculate the probability that more than three
of the selected marbles are red. Give your answer correct to two
decimal places.
P( 3 red) P (4 red) P (5 red)+P (6 red)
12. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
12
C3 12C3
P(3 red) 24
C6
0.3595
0.36 (to 2 dp)
(ii) Hence, or otherwise, calculate the probability that more than three
of the selected marbles are red. Give your answer correct to two
decimal places.
P( 3 red) P (4 red) P (5 red)+P (6 red)
12
C4 12C2 12C5 12C1 12C6 12C0
24
C6
13. 2007 Extension 2 HSC Q5a)
A bag contains 12 red marbles and 12 yellow marbles. Six marbles
are selected at random without replacement.
(i) Calculate the probability that exactly three of the selected marbles
are red. Give your answer correct to two decimal places.
12
C3 12C3
P(3 red) 24
C6
0.3595
0.36 (to 2 dp)
(ii) Hence, or otherwise, calculate the probability that more than three
of the selected marbles are red. Give your answer correct to two
decimal places.
P( 3 red) P (4 red) P (5 red)+P (6 red)
12
C4 12C2 12C5 12C1 12C6 12C0
24
C6
0.3202
0.32 (to 2 dp)
15. OR
P( 3 red) 1 P (3 red) P ( 3 red)
1 P (3 red) P ( 3 yellow)
16. OR
P( 3 red) 1 P (3 red) P ( 3 red)
1 P (3 red) P ( 3 yellow)
1 P (3 red) P ( 3 red)
17. OR
P( 3 red) 1 P (3 red) P ( 3 red)
1 P (3 red) P ( 3 yellow)
1 P (3 red) P ( 3 red)
2 P ( 3 red) 1 P(3 red)
18. OR
P( 3 red) 1 P (3 red) P ( 3 red)
1 P (3 red) P ( 3 yellow)
1 P (3 red) P ( 3 red)
2 P ( 3 red) 1 P(3 red)
1
P( 3 red) 1 P(3 red)
2
19. OR
P( 3 red) 1 P (3 red) P ( 3 red)
1 P (3 red) P ( 3 yellow)
1 P (3 red) P ( 3 red)
2 P ( 3 red) 1 P(3 red)
1
P( 3 red) 1 P(3 red)
2
1
1 0.3595
2
20. OR
P( 3 red) 1 P (3 red) P ( 3 red)
1 P (3 red) P ( 3 yellow)
1 P (3 red) P ( 3 red)
2 P ( 3 red) 1 P(3 red)
1
P( 3 red) 1 P(3 red)
2
1
1 0.3595
2
0.3202
0.32 (to 2 dp)
21. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
22. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
(i) How many different recordings are possible?
23. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
(i) How many different recordings are possible?
Recordings 3 3 3 3
24. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
(i) How many different recordings are possible?
Recordings 3 3 3 3
81
25. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
(i) How many different recordings are possible?
Recordings 3 3 3 3
81
(ii) Calculate the probability of the result which is recorded as WDLD.
26. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
(i) How many different recordings are possible?
Recordings 3 3 3 3
81
(ii) Calculate the probability of the result which is recorded as WDLD.
P WDLD 0.2 0.6 0.2 0.6
27. 2006 Extension 2 HSC Q5d)
In a chess match between the Home team and the Away team, a game is
played on board 1, board 2, board 3 and board 4.
On each board, the probability that the Home team wins is 0.2, the
probability of a draw is 0.6 and the probability that the Home team loses
is 0.2.
The results are recorded by listing the outcomes of the games for the
Home team in board order. For example, if the Home team wins on
board 2, draws on board 2, loses on board 3 and draws on board 4, the
result is recorded as WDLD.
(i) How many different recordings are possible?
Recordings 3 3 3 3
81
(ii) Calculate the probability of the result which is recorded as WDLD.
P WDLD 0.2 0.6 0.2 0.6
0.144
28. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
29. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
30. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
P 4 draws 0.64
0.1296
31. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
P 4 draws 0.64
0.1296
4!
P 2 wins, 2 losses 0.2 0.2
2 2
2!2!
0.0096
32. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
P 4 draws 0.64
0.1296 ways of arranging WWLL
4!
P 2 wins, 2 losses 0.2 0.2
2 2
2!2!
0.0096
33. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
P 4 draws 0.64
0.1296 ways of arranging WWLL
4!
P 2 wins, 2 losses 0.2 0.2
2 2
2!2!
0.0096
4!
P 1 win, 1 loss, 2 draws 0.2 0.2 0.6
2
2!
0.1728
34. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
P 4 draws 0.64
0.1296 ways of arranging WWLL
4!
P 2 wins, 2 losses 0.2 0.2
2 2
2!2!
0.0096 ways of arranging WLDD
4!
P 1 win, 1 loss, 2 draws 0.2 0.2 0.6
2
2!
0.1728
35. 1
(iii) Teams score 1 point for each game won, a point for each game
drawn and 0 points for each game lost. 2
What is the probability that the Home team scores more points than
the Away team?
first calculate probability of equal points
P 4 draws 0.64
0.1296 ways of arranging WWLL
4!
P 2 wins, 2 losses 0.2 0.2
2 2
2!2!
0.0096 ways of arranging WLDD
4!
P 1 win, 1 loss, 2 draws 0.2 0.2 0.6
2
2!
0.1728
P equal points 0.1296 0.0096 0.1728
0.312
37. P unequal points 1 0.312
0.688
As the probabilities are equally likely for the Home and Away teams,
then either the Home team has more points or the Away team has more
points.
38. P unequal points 1 0.312
0.688
As the probabilities are equally likely for the Home and Away teams,
then either the Home team has more points or the Away team has more
points.
1
P Home team more points P unequal points
2
39. P unequal points 1 0.312
0.688
As the probabilities are equally likely for the Home and Away teams,
then either the Home team has more points or the Away team has more
points.
1
P Home team more points P unequal points
2
1
0.688
2
0.344
40. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
41. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
42. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6
P( 400)
9
43. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
44. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
45. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
(ii) What is the probability that the digits are drawn in descending
order?
46. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
(ii) What is the probability that the digits are drawn in descending
order?
total arrangements of 3 digits 3!
47. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
(ii) What is the probability that the digits are drawn in descending
order?
total arrangements of 3 digits 3!
6
48. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
(ii) What is the probability that the digits are drawn in descending
order?
total arrangements of 3 digits 3!
6
Only one arrangement will be in descending order
49. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
(ii) What is the probability that the digits are drawn in descending
order?
total arrangements of 3 digits 3!
6
Only one arrangement will be in descending order
1
P descending order
6
50. 2002 Extension 2 HSC Q4c)
From a pack of nine cards numbered 1, 2, 3, …, 9, three cards are
drawn at random and laid on a table from left to right.
(i) What is the probability that the number exceeds 400?
6 it is the same as saying; “what is the
P( 400)
9 probability of the first number being >4”
2
3
(ii) What is the probability that the digits are drawn in descending
order?
total arrangements of 3 digits 3!
6
Only one arrangement will be in descending order
1
P descending order
6 Exercise 10H; odd