11.4 Probability
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This document discusses fundamentals of probability, including theoretical and empirical probability. It provides examples of calculating probabilities of events using formulas that take the number of outcomes of an event over the total number of possible outcomes. Examples include probabilities of rolling certain numbers on a die, being dealt certain cards, blood types based on parent genetics, and marital status based on US census data. Assignments are provided for classwork and homework problems.
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11.6 Probabilities Involving OR and NOT
1) The probability of an event not occurring is equal to 1 minus the probability of it occurring.
2) When events are mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities.
3) When events are not mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities minus the probability of them both occurring.
11.6 Probability Involving Or and Not
1) The probability of an event not occurring is equal to 1 minus the probability of it occurring.
2) When events are mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities.
3) When events are not mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities minus the probability of them both occurring.
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1) The probability of an event not occurring is equal to 1 minus the probability of it occurring.
2) When events are mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities.
3) When events are not mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities minus the probability of them both occurring.
11.6 Probability Involving Or and Not
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2) When events are mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities.
3) When events are not mutually exclusive, the probability of event A or B occurring is the sum of their individual probabilities minus the probability of them both occurring.
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Digging in to ProbabilityBernoullis Theorem If an experiment i.docx
Digging in to Probability
Bernoulli's Theorem: If an experiment is repeated a large number of times, the experimental probability of a particular outcome approaches a fixed number as the number of repetitions increases. (p.519)
1. Restate Bernoulli's Theorem in your own words (aimed at the level of an average nine year old).
2. If you have flipped a fair coin 99 times and gotten tails 79 of those 99 times, what is the chance that the next flip of the coin will come up tails? Why?
Experiment: Roll two distinguishable regular four-sided dice. The sides of each die are labeled 1,2,3, and 4. (You do not have to physically roll the dice. You will use this experiment for the rest of the worksheet.)
3. List all elements of the sample space. (Don't use a tree diagram unless you have to.)
4. Let G be the event that at least one die has a 3. List out the elements of event G. What do you think the probability of event G (written P(G)) is?
5. Let H be the event that both dice have even numbers. List out the elements of event H. What do you think P(H) is?
6. Let I be the event that the sum of the dice is 5. List out the elements of event I. What do you think P(I) is?
7. What is P(G
U
H)? What is P(G
U
I)? What is P(H
U
I)?
Two events are mutually exclusive if they have no elements in common. In other words, their intersection is empty.
8. Look at G;H; and I.
(a) Are G and H mutually exclusive?
(b) Are G and I mutually exclusive?
(c) Are H and I mutually exclusive?
9. Make a conjecture about P(A
U
B) for any generic events A and B that are mutually exclusive.
10. What is P(A
U
B) if A and B are NOT mutually exclusive?
11. Let J be the event that at least one die has an odd number. List out the elements of J. Which of G, H, and I is mutually exclusive to J? What is the probability of the union of that event with J?
Two events are complementary if they are mutually exclusive and P(A
U
B) = 1.
12. Without the concept of probability describe in your own words what it means for two events to be complementary?
Introduction to Probability
Probabilities are ratios. These ratios can be expressed as fractions, decimals, or percents. As the book says, these ratios are based on “outcomes of experiments". But what does this mean? We will explore the idea with an example.
Example: You have 4 colors of socks in your drawer: white, black, red, and gray. You reach in and pull out a sock.
1. What are the possible outcomes of your experiment?
The set of all possible outcomes is called the
Sample Space.
Often times, a sample space can be represented with a tree diagram.
2. What is the sample space if you pull out one sock, record its color, put it back, and then pull out another sock and record its color?
3. Choose a few outcomes from your sample space in question (2).
Any subset of a sample space is called an
Event
.
4. If there are exactly two of each color of sock, what are the chances of your chosen event from (3).
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2) Simple examples of calculating probability include throwing a die, where each number has a 1/6 probability, and drawing a card from a deck, where the probability depends on the specific card (e.g. 1/52 for a specific card).
3) Probability rules include the probability of two events occurring being the product of their individual probabilities, and the probability of one or the other occurring being the sum of individual probabilities minus their intersection.
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Discrete Probability Distributions
1.A group of people were asked if they had run a red light in the last year. 446 responded "yes", and 344 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal to 4 decimal places
2. A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?
The amount of rain, in inches, that will fall next Friday in Dallas, TX.
The major of a randomly drawn student from Arizona State University.
The number of books purchased next year by your local library.
i only
ii only
iii only
i and iii
ii and iii
i, ii, and iii
3. For families with 5 children, let XX be the number of children with Genetic Condition B. Can the following table be a probability distribution for the random variable XX?
xx
P(x)P(x)
1
0.2842
2
0.0923
3
0.2544
4
0.1366
5
0.1097
· no
· yes
4. Assume that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
xx
P(x)P(x)
0
0+
1
0+
2
0.0001
3
0.0011
4
0.0063
5
0.0246
6
0.0704
7
0.1477
8
0.2261
9
0.246
10
0.1807
11
0.0804
12
0.0164
Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x=7)=P(x=7)=
Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x≤7)=P(x≤7)=
Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
· yes
· no
5.
Probability
Scores
0.05
3
0.45
8
0.05
10
0.35
12
0.1
13
Find the expected value of the above random variable.
6. On a 9 question multiple-choice test, where each question has 3 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
7. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
7
10
2
19
Female
17
16
18
51
Total
24
26
20
70
If one student was chosen at random,
find the probability that the student got a B.
Give your answer as a fraction or decimal.
8. The table summarizes results from 989 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated?
Pedestrian Intoxicated?
Yes
No
Yes
45
75
No
281
588
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
9. Determine whether this table represents a probability d.
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This document discusses various concepts in probability, including empirical and theoretical probability, compound events, addition and multiplication rules, dependent and independent events, and counting principles. It provides examples to illustrate key probability concepts such as determining the probability of drawing certain cards or dice outcomes, compound events involving simple events, and rules for calculating probabilities of independent and dependent compound events.
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35818 Topic Discussion7Number of Pages 1 (Double Spaced).docx
- Emily scored one standard deviation above the mean on a standardized reading test.
- The normal curve can help understand this by showing that about 34% of children scored lower than Emily, and about 16% scored higher.
- A standard deviation above the mean means Emily scored higher than approximately 84% of other children who took the test.
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4.1-4.2 Sample Spaces and Probability
The document defines key concepts in probability theory, such as probability experiments, outcomes, sample spaces, events, classical probability, empirical probability, and subjective probability. It provides examples of how to calculate probabilities of simple and compound events using classical probability methods, including determining probabilities using fractions or decimals and interpreting "and" and "or" probabilities.
35819 Topic Discussion8Number of Pages 1 (Double Spaced).docx
35819 Topic: Discussion8
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will upload the instruction
Discussion: Discuss, elaborate and give example.
Author: (Jackson, S. L. (2017). Statistics Plain and Simple, 4th Edition. Cengage Learning.)
Use this author as reference. I uploaded also the full text below.
Instructions:
Emily is a fifth-grade student who completed a standardized reading test. She scored one standard deviation above the mean score.
Answer the following questions:
· How does the normal curve help you understand what this means about how Emily compares to other children who took the test? Explain how you determined your findings.
· How many children scored lower than Emily?
· How many children scored higher?
Reference:
Basic Probability Concepts
The Rules of Probability
Probability and the Standard Normal Distribution
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Module 8: Hypothesis Testing and Inferential Statistics
Null and Alternative Hypotheses
Two-Tailed and One-Tailed Hypothesis Tests
Type I and Type II Errors in Hypothesis Testing
Probability, Statistical Significance, and Errors
Using Inferential Statistics
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Chapter 4 Summary and Review
In this chapter you will be introduced to the concepts of probability and hypothesis testing. Probability is the study of likelihood and uncertainty. Most decisions that we make are probabilistic in nature. Thus, probability plays a critical role in most professions and in our everyday decisions. We will discuss basic probability concepts along with how to compute probabilities and the use of the standard normal curve in making probabilistic decisions.
probability The study of likelihood and uncertainty; the number of ways a particular outcome can occur, divided by the total number of outcomes.
Hypothesis testing is the process of determining whether a hypothesis is supported by the results of a research project. Our introduction to hypothesis testing will include a discussion of the null and alternative hypotheses, Type I and Type II errors, and one- and two-tailed tests of hypotheses as well as an introduction to statistical significance and probability as they relate to inferential statistics.
hypothesis testing The process of determining whether a hypothesis is supported by the results of a research study.
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Probability
Learning Objectives
•Understand how probability is used in everyday life.
•Know how to compute a probability.
•Understand and be able to apply the multiplication rule.
•Understand and be able to apply the addition rule.
•Understand the relationship between the standard normal curve and probability.
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AM40SFeb19
In a family with 3 children, the probability that 2 of the children will be girls can be calculated as follows:
There are 3 children and each child can be either a boy or a girl. So there are 2 possible outcomes for each child. Using the fundamental principle of counting, there are 2 * 2 * 2 = 8 possible combinations of boys and girls. Out of these 8 combinations, 3 combinations will have exactly 2 girls. Therefore, the probability that 2 of the 3 children will be girls is 3/8.
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Bernoulli's Theorem: If an experiment is repeated a large number of times, the experimental probability of a particular outcome approaches a fixed number as the number of repetitions increases. (p.519)
1. Restate Bernoulli's Theorem in your own words (aimed at the level of an average nine year old).
2. If you have flipped a fair coin 99 times and gotten tails 79 of those 99 times, what is the chance that the next flip of the coin will come up tails? Why?
Experiment: Roll two distinguishable regular four-sided dice. The sides of each die are labeled 1,2,3, and 4. (You do not have to physically roll the dice. You will use this experiment for the rest of the worksheet.)
3. List all elements of the sample space. (Don't use a tree diagram unless you have to.)
4. Let G be the event that at least one die has a 3. List out the elements of event G. What do you think the probability of event G (written P(G)) is?
5. Let H be the event that both dice have even numbers. List out the elements of event H. What do you think P(H) is?
6. Let I be the event that the sum of the dice is 5. List out the elements of event I. What do you think P(I) is?
7. What is P(G
U
H)? What is P(G
U
I)? What is P(H
U
I)?
Two events are mutually exclusive if they have no elements in common. In other words, their intersection is empty.
8. Look at G;H; and I.
(a) Are G and H mutually exclusive?
(b) Are G and I mutually exclusive?
(c) Are H and I mutually exclusive?
9. Make a conjecture about P(A
U
B) for any generic events A and B that are mutually exclusive.
10. What is P(A
U
B) if A and B are NOT mutually exclusive?
11. Let J be the event that at least one die has an odd number. List out the elements of J. Which of G, H, and I is mutually exclusive to J? What is the probability of the union of that event with J?
Two events are complementary if they are mutually exclusive and P(A
U
B) = 1.
12. Without the concept of probability describe in your own words what it means for two events to be complementary?
Introduction to Probability
Probabilities are ratios. These ratios can be expressed as fractions, decimals, or percents. As the book says, these ratios are based on “outcomes of experiments". But what does this mean? We will explore the idea with an example.
Example: You have 4 colors of socks in your drawer: white, black, red, and gray. You reach in and pull out a sock.
1. What are the possible outcomes of your experiment?
The set of all possible outcomes is called the
Sample Space.
Often times, a sample space can be represented with a tree diagram.
2. What is the sample space if you pull out one sock, record its color, put it back, and then pull out another sock and record its color?
3. Choose a few outcomes from your sample space in question (2).
Any subset of a sample space is called an
Event
.
4. If there are exactly two of each color of sock, what are the chances of your chosen event from (3).
Probability logics
1) Probability is a measure of the likelihood of an event occurring, defined as the number of favorable outcomes divided by the total number of possible outcomes.
2) Simple examples of calculating probability include throwing a die, where each number has a 1/6 probability, and drawing a card from a deck, where the probability depends on the specific card (e.g. 1/52 for a specific card).
3) Probability rules include the probability of two events occurring being the product of their individual probabilities, and the probability of one or the other occurring being the sum of individual probabilities minus their intersection.
Probability basics and bayes' theorem
It gives detail description about probability, types of probability, difference between mutually exclusive events and independent events, difference between conditional and unconditional probability and Bayes' theorem
STAT: Probability (continuation)(2)
This document contains examples and exercises on probability and conditional probability. It introduces concepts like independent and dependent events, and how to calculate probabilities of events occurring together or in sequence using multiplication rules. Some examples include calculating the probability of drawing certain cards from a deck, rolling dice with specific outcomes, and patients consulting different doctors. The exercises practice finding probabilities and conditional probabilities for scenarios involving balls in boxes, births at a hospital, and light bulbs in different boxes.
Introduction to probability
This document provides an introduction to key concepts in probability including random processes, outcomes that are disjoint vs. non-disjoint, independence, probability distributions, and applying rules of probability to calculate probabilities of events. It includes examples such as the probability of drawing certain cards from a deck and the probability of Texans being uninsured based on survey data. Formulas for calculating probabilities of unions, intersections, and conditional probabilities are presented along with checks for independence between variables.
Discrete Probability Distributions1.A group of people were.docx
Discrete Probability Distributions
1.A group of people were asked if they had run a red light in the last year. 446 responded "yes", and 344 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal to 4 decimal places
2. A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?
The amount of rain, in inches, that will fall next Friday in Dallas, TX.
The major of a randomly drawn student from Arizona State University.
The number of books purchased next year by your local library.
i only
ii only
iii only
i and iii
ii and iii
i, ii, and iii
3. For families with 5 children, let XX be the number of children with Genetic Condition B. Can the following table be a probability distribution for the random variable XX?
xx
P(x)P(x)
1
0.2842
2
0.0923
3
0.2544
4
0.1366
5
0.1097
· no
· yes
4. Assume that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
xx
P(x)P(x)
0
0+
1
0+
2
0.0001
3
0.0011
4
0.0063
5
0.0246
6
0.0704
7
0.1477
8
0.2261
9
0.246
10
0.1807
11
0.0804
12
0.0164
Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x=7)=P(x=7)=
Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x≤7)=P(x≤7)=
Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
· yes
· no
5.
Probability
Scores
0.05
3
0.45
8
0.05
10
0.35
12
0.1
13
Find the expected value of the above random variable.
6. On a 9 question multiple-choice test, where each question has 3 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
7. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
7
10
2
19
Female
17
16
18
51
Total
24
26
20
70
If one student was chosen at random,
find the probability that the student got a B.
Give your answer as a fraction or decimal.
8. The table summarizes results from 989 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated?
Pedestrian Intoxicated?
Yes
No
Yes
45
75
No
281
588
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
9. Determine whether this table represents a probability d.
Probability 2
This document discusses various concepts in probability, including empirical and theoretical probability, compound events, addition and multiplication rules, dependent and independent events, and counting principles. It provides examples to illustrate key probability concepts such as determining the probability of drawing certain cards or dice outcomes, compound events involving simple events, and rules for calculating probabilities of independent and dependent compound events.
01_Probability of Simple Events.ppt
PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.VPROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.VVPROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS POWERPOINT PRESENTATION.PROBABILITY OF SIMPLE EVENTS
35818 Topic Discussion7Number of Pages 1 (Double Spaced).docx
- Emily scored one standard deviation above the mean on a standardized reading test.
- The normal curve can help understand this by showing that about 34% of children scored lower than Emily, and about 16% scored higher.
- A standard deviation above the mean means Emily scored higher than approximately 84% of other children who took the test.
Chapter 0: the what and why of statistics
First set of slides for my L3 course Statistics (1): Estimation at Université Paris-Dauphine 2014-2015
4.1-4.2 Sample Spaces and Probability
The document defines key concepts in probability theory, such as probability experiments, outcomes, sample spaces, events, classical probability, empirical probability, and subjective probability. It provides examples of how to calculate probabilities of simple and compound events using classical probability methods, including determining probabilities using fractions or decimals and interpreting "and" and "or" probabilities.
35819 Topic Discussion8Number of Pages 1 (Double Spaced).docx
35819 Topic: Discussion8
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will upload the instruction
Discussion: Discuss, elaborate and give example.
Author: (Jackson, S. L. (2017). Statistics Plain and Simple, 4th Edition. Cengage Learning.)
Use this author as reference. I uploaded also the full text below.
Instructions:
Emily is a fifth-grade student who completed a standardized reading test. She scored one standard deviation above the mean score.
Answer the following questions:
· How does the normal curve help you understand what this means about how Emily compares to other children who took the test? Explain how you determined your findings.
· How many children scored lower than Emily?
· How many children scored higher?
Reference:
Basic Probability Concepts
The Rules of Probability
Probability and the Standard Normal Distribution
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Module 8: Hypothesis Testing and Inferential Statistics
Null and Alternative Hypotheses
Two-Tailed and One-Tailed Hypothesis Tests
Type I and Type II Errors in Hypothesis Testing
Probability, Statistical Significance, and Errors
Using Inferential Statistics
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Chapter 4 Summary and Review
In this chapter you will be introduced to the concepts of probability and hypothesis testing. Probability is the study of likelihood and uncertainty. Most decisions that we make are probabilistic in nature. Thus, probability plays a critical role in most professions and in our everyday decisions. We will discuss basic probability concepts along with how to compute probabilities and the use of the standard normal curve in making probabilistic decisions.
probability The study of likelihood and uncertainty; the number of ways a particular outcome can occur, divided by the total number of outcomes.
Hypothesis testing is the process of determining whether a hypothesis is supported by the results of a research project. Our introduction to hypothesis testing will include a discussion of the null and alternative hypotheses, Type I and Type II errors, and one- and two-tailed tests of hypotheses as well as an introduction to statistical significance and probability as they relate to inferential statistics.
hypothesis testing The process of determining whether a hypothesis is supported by the results of a research study.
MODULE 7
Probability
Learning Objectives
•Understand how probability is used in everyday life.
•Know how to compute a probability.
•Understand and be able to apply the multiplication rule.
•Understand and be able to apply the addition rule.
•Understand the relationship between the standard normal curve and probability.
In order to better understand the nature of probabilistic decisions, consider the following court.
Pre-Cal 40S June 1, 2009
The document discusses medical testing and provides probabilities for the outcomes of different medical tests. It notes that a test for cancer is known to be 98% accurate and that 0.5% of the population has cancer. It then poses the question - what is the probability that a person who tests positive for cancer actually has cancer? To answer this, it outlines the four possible outcomes when 1,000,000 people are tested: those with cancer who test positive, those with cancer who test negative, those without cancer who test positive, and those without cancer who test negative. It provides a framework to calculate how many people would fall into each category based on the given accuracy rates and prevalence of cancer in the population.
PROBABILITY BY ZOEN CUTE KAAYO SA KATANAN.pptx
Probability is a branch of mathematics that enables us to predict the occurrence of an event as a result of an experiment. The probability of an event is calculated by taking the number of outcomes in the event and dividing it by the total number of possible outcomes. Simple events consist of a single outcome, while compound events consist of two or more simple events. Examples of calculating probability are given for simple events like rolling a die or drawing balls from a jar, and compound events like rolling two dice. The importance of probability in decision making in real life is discussed.
Probability and chance (math)
This document provides information about probability and chance. It defines probability as a measure of how likely an event is to occur from 0 to 1. It gives examples of probability using a spinner and explains probability activities using M&Ms. Chance is defined as the likelihood something will happen from 0 to 100%. Examples are given comparing the chance of rain at 50% versus 80%. Questions are provided to practice calculating probabilities and chances.
THE ADDITION RULES FOR PROBABILITY.pptx
This document discusses probability rules for addition when events are mutually exclusive or not mutually exclusive. It provides examples of applying the addition rules to calculate probabilities. For mutually exclusive events A and B, the probability of A or B is P(A) + P(B). For non-mutually exclusive events, the probability is P(A) + P(B) - P(A and B). The document also discusses examples of mutually exclusive and non-mutually exclusive events using dice rolls, card draws, and real world scenarios. It provides a quiz with probability calculation problems applying the addition rules.
Pedigree Basics!
Pedigrees are like family trees that show the transmission of traits and diseases between generations. They indicate whether a trait is dominant or recessive and if it is transmitted on an autosome or the X chromosome. Pedigrees use symbols to represent individuals and their genotypes or phenotypes. An example pedigree is analyzed to determine the genotypes of each individual based on their offspring. Practice problems are given to allow interpretation of pedigrees related to traits such as the ability to roll the tongue or cause albinism.
Please- answers all my question is for genetic class 3- Describe the.docx
Please, answers all my question is for genetic class
3. Describe the pattern of inheritance shown in the pedigree below, giving evidence to support your answer. Give the genotypes for individuals II-2, II-4 and II-2. Include a legend for the symbols used. (10 marks) Describe the pattern of inheritance shown in the pedigree below, giving evidence to support your answer. Give the genotypes for individuals II-4, II-7 and III-7. Include a legend for the symbols used. ( 10 marks) 5. A type of hemophilia is due to an X-linked recessive allele. An affected man whose phenotype has been successfully managed now has children with a woman who is a carrier. Providing a legend for your, answer the following questions: a. What are the genotypes of the mother and father? (1 mark) b. What are the probabilities that i. a child will be affected with hemophilia. ii. a child is a carrier. iii. their daughter is a carrier. iv. their male fetus will be affected. (4 marks) 6. Genes for two different recessive disorders are linked on the X chromosome; they are 26 map units apart. A woman is a carrier for both disorder A and disorder B , with the alleles for these genes in cis. Her husband has normal alleles for both of these genes. The woman is pregnant with their first son. What is the probability (in percent) this son is affected with both disorders? Explain, showing the proportions and types of the woman's gametes and identifying them as parental or recombinant. (5 marks) 7. In certain human matings of albino and black-haired parents, the offspring are always blackhaired. When these black-haired offspring of the different families mate with each other (non-consanguineously) and their children are pooled to get significant data, these are the children's phenotypic proportions: 9 black-haired children 3 brown-haired children 4 albino children a. How many genes are involved in this trait? b. How many alleles of each gene are there? c. What type of gene interaction is occurring for this trait? Describe it. d. What are the genotypes of the initial albino and black-haired parents? Provide a legend. e. What are the genotypes of their offspring (all black-haired)? f. What are the genotypes and the specific proportions of the albino children in the third generation? g. What are the genotypes of the brown-haired children? 8. Which type of chromosomal aneuploidy typically has less severe effects on an individual: sex chromosome aneuploidy or autosomal aneuploidy? Explain why. (4 marks) 9. An organism has six chromosomes in its somatic cells. Determine the number of gametes with different chromosome compositions that this organism can potentially create. Explain your answer, including the genetic basis for your calculation. Ignore the allelic variation created by crossing over. ( 4 marks) 10. Compare the inheritance and transmission of Xlinked genes with that of mitochondrial genes. (4 marks) 11. A woman has a normal number of fingers and toes. She has many relatives with ex.
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How to Build a Module in Odoo 17 Using the Scaffold Method
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Liberal Approach to the Study of Indian Politics.pdf
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Azure Interview Questions and Answers PDF By ScholarHat
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Film vocab for eal 3 students: Australia the movie
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Pride Month Slides 2024 David Douglas School District
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Walmart Business+ and Spark Good for Nonprofits.pdf
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RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
11.4 Probability
- 1. 11.4 Fundamentals of Probability
- 2. Some important questions What is probability? Why study probability? What is the probability of winning the Maryland lottery? What is the probability of being struck by a lightning? What is the probability of getting an A in the class?
- 3. Computing Theoretical Probability If an event E has n(E) equally-likely outcomes and its sample space S has n(s) equally-likely outcomes, the theoretical probability of event E, denoted by P(E) is P(E) = number of outcomes in event E = n(E) total # of possible outcomes n(S)
- 4. Example 1 A die is rolled once. Find the probability of getting: a. 5 b. an even number c. a number greater than 2 d. a number less than 6 e. a number greater than 4
- 5. Example 2 You are dealt a standard 52-card deck. Find the probability of being dealt A. A king B. A red card C. A five D. A picture card E. A red queen F. A club
- 6. Probabilities in Genetics Blood type problem: What is the chance of having a blood type AB if your parents have types AO and BB. Dimples: Facial dimples are examples of dominant genes which means that if a person has genotype DD or Dd, he or she will have a dimple. A person with no dimple has a genotype of dd. What is the chance of producing an offspring with a dimple if one parent has a dimple and the other has none?
- 7. Empirical Probability Theoretical probability is based on a set of equally-likely outcomes and the number of elements in a set. By contrast, empirical probability applies to situations in which we observe the frequency of occurrence of an event. P (E) = observed number of times E occurs total number of observed occurences
- 8. Example Marital Status of the US Population , Ages 18 or older in millions Source: US Census Bureau
- 9. Questions: What is the probability of randomly selecting a female? What is the probability of randomly selecting a divorced person? What is the probability of randomly selecting a married male?
- 10. Assignments Classwork: Checkpoints 1-4 p. 580-584 And do #s 2-30 (evens) HW: p. 585-586, #s 1-39 (odd); 49-63 (odd)