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The document defines key probability terms like experiment, trial, outcome, sample space, event, and probability. It provides examples of calculating probabilities of individual outcomes and combined events by adding the probabilities of relevant outcomes. The document explains that the probabilities of all outcomes in a sample space must add up to 1.
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Experimental probability pp
The document discusses experimental probability and how it is calculated by performing trials of an experiment and recording the number of successful outcomes. It provides examples of calculating experimental probability based on rolling dice and cars moving in a race based on dice rolls. The document aims to help students understand what experimental probability means, become familiar with experimenting with chance, and compare experimental and actual probability.
Grade 8 Probability Cambridge [PPT]
PROBABILITY FOR MIDDLE SCHOOL
Topics :
• The probability that an outcome does not happen
• Equally likely outcomes
• Listing all possible outcomes
• Experimental and theoretical probabilities
//&//
Experimental Probability
The document defines key terms related to experimental probability such as experiment, outcome, and sample space. It provides examples of identifying the sample space and outcomes for experiments involving coin flips and rolling a die. The formula for calculating experimental probability is given as the number of times an event occurred divided by the total number of trials. An example is shown of a student calculating the probability of a coin landing on heads based on 30 coin flip trials.
Probability class 9 ____ CBSE
This document discusses probability and related concepts. It defines probability as the study of uncertainty and notes its uses in fields like mathematics, science, and medicine. Key terms are introduced, including random experiments, trials, events, and elementary events. Experimental probability is defined based on the number of trials and outcomes. Examples are provided to demonstrate calculating probabilities and the relationship that the probabilities of all elementary events sum to 1.
Unit 11.2 theoretical probability
This document provides an overview of theoretical probability concepts including:
- Theoretical probability is calculated as the number of favorable outcomes divided by the total number of equally likely outcomes.
- Experiments are considered "fair" if all outcomes are equally likely.
- The probability of an event occurring plus the probability of it not occurring equals 1.
- Complement probability refers to outcomes not included in the main event.
- Odds can be used to express likelihood and converted to and from probabilities using ratios of favorable to total outcomes.
Probability
This document discusses theoretical and experimental probability. It provides examples of calculating probabilities from experiments and outcomes. Some key points:
- An experiment of tossing a coin 1000 times resulted in 520 heads and 480 tails, giving experimental probabilities of 0.52 for heads and 0.48 for tails.
- Theoretical probabilities can be calculated by considering all possible outcomes and the number of favorable outcomes. For example, the probability of getting at least one head when tossing two coins is 3/4.
- Complementary events have probabilities that sum to 1, so the probability of an event can be found by subtracting its complement's probability from 1.
- Examples demonstrate calculating probabilities from the number of favorable outcomes for different
Negative binomial distribution
1. A negative binomial experiment consists of repeated trials that result in one of two outcomes (success/failure). It continues until a fixed number (k) of successes occur.
2. The probability of success (p) is constant across trials, which are independent. The number of trials (x) needed to achieve k successes follows a negative binomial distribution.
3. The document provides the notation and formula for the negative binomial distribution. It also gives examples of calculating the probability of achieving k successes in x trials under this distribution.
Unit 11.2 experimental probability
This document provides an overview of experimental probability:
- It defines key terms like experiment, trial, outcome, and sample space.
- It explains how to calculate experimental probability by taking the number of times an event occurs over the total number of trials.
- It discusses how experimental probability can be used to make predictions about future experiments based on past results.
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Experimental probability pp
The document discusses experimental probability and how it is calculated by performing trials of an experiment and recording the number of successful outcomes. It provides examples of calculating experimental probability based on rolling dice and cars moving in a race based on dice rolls. The document aims to help students understand what experimental probability means, become familiar with experimenting with chance, and compare experimental and actual probability.
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PROBABILITY FOR MIDDLE SCHOOL
Topics :
• The probability that an outcome does not happen
• Equally likely outcomes
• Listing all possible outcomes
• Experimental and theoretical probabilities
//&//
Experimental Probability
The document defines key terms related to experimental probability such as experiment, outcome, and sample space. It provides examples of identifying the sample space and outcomes for experiments involving coin flips and rolling a die. The formula for calculating experimental probability is given as the number of times an event occurred divided by the total number of trials. An example is shown of a student calculating the probability of a coin landing on heads based on 30 coin flip trials.
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Unit 11.2 theoretical probability
This document provides an overview of theoretical probability concepts including:
- Theoretical probability is calculated as the number of favorable outcomes divided by the total number of equally likely outcomes.
- Experiments are considered "fair" if all outcomes are equally likely.
- The probability of an event occurring plus the probability of it not occurring equals 1.
- Complement probability refers to outcomes not included in the main event.
- Odds can be used to express likelihood and converted to and from probabilities using ratios of favorable to total outcomes.
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This document discusses theoretical and experimental probability. It provides examples of calculating probabilities from experiments and outcomes. Some key points:
- An experiment of tossing a coin 1000 times resulted in 520 heads and 480 tails, giving experimental probabilities of 0.52 for heads and 0.48 for tails.
- Theoretical probabilities can be calculated by considering all possible outcomes and the number of favorable outcomes. For example, the probability of getting at least one head when tossing two coins is 3/4.
- Complementary events have probabilities that sum to 1, so the probability of an event can be found by subtracting its complement's probability from 1.
- Examples demonstrate calculating probabilities from the number of favorable outcomes for different
Negative binomial distribution
1. A negative binomial experiment consists of repeated trials that result in one of two outcomes (success/failure). It continues until a fixed number (k) of successes occur.
2. The probability of success (p) is constant across trials, which are independent. The number of trials (x) needed to achieve k successes follows a negative binomial distribution.
3. The document provides the notation and formula for the negative binomial distribution. It also gives examples of calculating the probability of achieving k successes in x trials under this distribution.
Unit 11.2 experimental probability
This document provides an overview of experimental probability:
- It defines key terms like experiment, trial, outcome, and sample space.
- It explains how to calculate experimental probability by taking the number of times an event occurs over the total number of trials.
- It discusses how experimental probability can be used to make predictions about future experiments based on past results.
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This document provides an introduction to probability. It defines probability as the numerical description of how likely an event is to occur or a proposition is true. Some common applications of probability are weather forecasting, coin flipping, lottery tickets, and playing cards. The document then discusses basic probability concepts, defining an experiment as any process with two or more outcomes, and an outcome as the result of a single trial. An event is a collection of outcomes, and a sample space is the set of all possible outcomes. It provides examples of experiments, outcomes, events, and sample spaces for rolling a die and tossing a coin twice.
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This document discusses theoretical probability and related concepts such as experimental probability, odds, and converting between probabilities and odds. It provides examples of calculating theoretical probabilities of outcomes for experiments involving items like number cubes, coins, and spinners. It also demonstrates using the complement and sum of probabilities to find an unknown probability, as well as converting between probabilities and odds. The document is intended to teach these probability concepts and provide practice problems to test understanding.
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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.
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The document discusses key concepts in probability theory including:
1. Probability theory provides tools to quantify uncertainties and assign probabilities using classical, relative frequency, and subjective approaches.
2. Key probability terms are defined such as experiment, event, sample space, independent and dependent events, mutually exclusive events, and union, intersection, and complement of events.
3. Basic probability rules are covered including the multiplication rule for independent events, addition rule for mutually exclusive events, and how to calculate the probability of events.
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3. Statistical analysis methods are introduced including how to estimate the mean and variance from samples from a distribution.
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The document provides an overview of probability concepts including:
- Probability is a measure of how likely an event is, defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Theoretical probability predicts outcomes without performing experiments, dealing with events as combinations of elementary outcomes.
- Random experiments may have different results each time while deterministic experiments always produce the same outcome.
- Elementary events are individual outcomes, and compound events combine multiple elementary outcomes.
- Theoretical probability of an event is the number of favorable elementary events divided by the total number of possible events.
- The probabilities of an event and its negation must sum to 1.
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This document provides an overview of key concepts in probability. It defines probability as a measure of likelihood or chance that can be estimated using relative frequency or subjective estimates. It introduces common probability notation and outlines three basic rules for computing probability: relative frequency approximation, classical approach, and subjective probabilities. Examples are provided to illustrate these concepts and rules. The document also discusses the law of large numbers, probability limits between 0 and 1, and guidelines for rounding off probabilities.
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This document discusses theoretical probability and related concepts such as experimental probability, odds, and converting between probabilities and odds. It provides examples of calculating theoretical probabilities of outcomes for experiments involving items like number cubes, coins, and spinners. It also demonstrates using the complement and sum of probabilities to find an unknown probability, as well as converting between probabilities and odds. The document is intended to teach these probability concepts and provide practice problems to test understanding.
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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.
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This is benefical for student mainly for class 10. And the ppt material is extracted from R.D. Sharma and 10 NCERT Text book.
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This slide presentation is a non-technical introduction to the concept of probability. The level of the presentation would be most suitable for college students majoring in business or a related field, but it could also be used in high school classes.
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This document provides an overview of key concepts in probability. It defines probability as the likelihood of an event occurring, expressed as a number between 0 and 1. It discusses common probability terms like experiment, outcome, sample space, event, and sample point. It also covers different types of probability like classical, statistical, and subjective probability. Additionally, it explains concepts like independent and mutually exclusive events, conditional probability, and Bayes' theorem. It concludes by discussing some applications of probability in fields like statistics, biology, information theory, and operations research.
03+probability+distributions.ppt
The document discusses key concepts in probability theory including:
1. Probability theory provides tools to quantify uncertainties and assign probabilities using classical, relative frequency, and subjective approaches.
2. Key probability terms are defined such as experiment, event, sample space, independent and dependent events, mutually exclusive events, and union, intersection, and complement of events.
3. Basic probability rules are covered including the multiplication rule for independent events, addition rule for mutually exclusive events, and how to calculate the probability of events.
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1. The document discusses basic concepts in probability and statistics, including sample spaces, events, probability distributions, and random variables.
2. Key concepts are explained such as independent and conditional probability, Bayes' theorem, and common probability distributions like the uniform and normal distributions.
3. Statistical analysis methods are introduced including how to estimate the mean and variance from samples from a distribution.
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The document provides an overview of probability concepts including:
- Probability is a measure of how likely an event is, defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Theoretical probability predicts outcomes without performing experiments, dealing with events as combinations of elementary outcomes.
- Random experiments may have different results each time while deterministic experiments always produce the same outcome.
- Elementary events are individual outcomes, and compound events combine multiple elementary outcomes.
- Theoretical probability of an event is the number of favorable elementary events divided by the total number of possible events.
- The probabilities of an event and its negation must sum to 1.
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This document provides an overview of key concepts in probability. It defines probability as a measure of likelihood or chance that can be estimated using relative frequency or subjective estimates. It introduces common probability notation and outlines three basic rules for computing probability: relative frequency approximation, classical approach, and subjective probabilities. Examples are provided to illustrate these concepts and rules. The document also discusses the law of large numbers, probability limits between 0 and 1, and guidelines for rounding off probabilities.
Scientific Number
The document provides rules and guidelines for writing numbers in science, including:
1. When writing large numbers, use spaces instead of commas and include leading zeros for decimals.
2. Scientific notation is an easy way to write very large or small numbers, where the number is written as the product of a number between 1 and 10 and an exponent of 10.
3. Rules for scientific notation include having the exponent be a whole number so the number is between 1 and 10, and the exponent equals the number of decimal places moved. Negative exponents are used for numbers between 0 and 1.
Poisson Distribution
Poisson's distribution describes the probability of a given number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event. The probability of x events occurring is calculated using the formula P(x)= (ux e-u)/x!, where u is the average number of events and e is the mathematical constant approximately equal to 2.718. The mean and variance of a Poisson distribution are both equal to u. The distribution can be used to calculate probabilities of occurrences like defective products, accidents, or births given the average rates of such events.
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Scientific notation is used to express very large or small numbers. It involves moving the decimal point in a number to the right or left by a power of 10. Positive powers of 10 move the decimal point right to express large numbers, like distances between planets. Negative powers of 10 move the decimal point left to express small decimal numbers, like distances between atoms. To convert a number to scientific notation, the decimal is moved to create a number between 1 and 10, and the power of 10 indicates how many places the decimal was moved.
Percents!
This document discusses percents and how to convert between percents, fractions, and decimals. It provides examples of converting between different representations of ratios and finding the percent of a number. Real world applications of percents like tips, taxes, and test grades are used to demonstrate common uses. Formulas and steps are given for converting between fractions and percents, writing probabilities as percents, and finding the percent of a given number.
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Solve Percentages
This document provides examples and explanations of percentage calculations and tricks. It begins by defining key terms like numbers, ratios, fractions, and percentages. It then provides 21 example problems demonstrating how to use percentages to solve word problems involving topics like profit/loss, population changes, exam scores, and more. The examples illustrate common percentage calculation methods and tricks like breaking percentages into fractions. The document emphasizes learning fractions and tables to help solve percentage problems more quickly.
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- Questions are posed about whether scenarios are possible, like certain state territories, and definitions are given, such as what the continental divide is.
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2. Domestically, Jurassic World is ranked 5th on the North American box office top 10 list after only a few weeks.
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Application of mathematics in sports
Maths is not only used in science it can also used in many field like sports, music economics dance..........
Schools as Learning Playgrounds
My books- Learning to Go https://gum.co/learn2go & The 30 Goals Challenge for Teachers http://amazon.com/The-Goals-Challenge-Teachers-Transform/dp/0415735343
Resources at http://shellyterrell.com/playgrounds
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- Probability trees can model multiple dependent or independent events.
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The document defines probability as a numerical measure of the likelihood of an event occurring. It discusses the history of probability and how values are assigned on a scale from 0 to 1. Experiments are defined as processes that generate outcomes, and the probability of an event is the number of ways it can occur divided by the total number of possible outcomes. An important rule is that the probabilities of all outcomes must sum to 1.
(7) Lesson 9.2
The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
There are 6 possible ways to roll a sum of 10: (1,9), (2,8), (3,7), (4,6), (5,5), (6,4).
There are 6 combinations that result in a sum of 10 out of the total possible combinations when rolling two number cubes, which is 6^2 = 36 possible outcomes.
Therefore, the theoretical probability is 5/36.
Applied 40S March 1, 2009
Review: experimental vrs. theoretical probability, designing simulations, using the randBin() command on the TI-83, calculating theoretical probabilities using "and" and "or".
group4-randomvariableanddistribution-151014015655-lva1-app6891 (1).pdf
This document discusses random variables and probability distributions. It introduces two types of random variables - discrete and continuous. Discrete random variables can take on countable values, like the number of people in line, while continuous random variables can take any value in an interval, like time or weight. The document covers probability distributions for discrete random variables, including the binomial and Poisson distributions. It also discusses expected values, variance, and the hypergeometric distribution for sampling without replacement.
group4-randomvariableanddistribution-151014015655-lva1-app6891.pdf
This document discusses probability distributions for discrete random variables. It introduces the concepts of discrete and continuous random variables and gives examples of each. Probability distributions describe the probabilities associated with all possible outcomes of a random variable. The chapter covers the binomial, Poisson, and hypergeometric distributions. It defines key terms like mean, variance, and expected value and provides examples of how to calculate probabilities using these various distributions.
What are the chances? - Probability
The document discusses probability theory and its applications. It begins with everyday examples of probability, then describes the origins of probability theory through the correspondence of Blaise Pascal and Pierre de Fermat. It defines key probability concepts and terms. It provides examples of calculating probabilities of events, including conditional probabilities and combined events. It discusses using relative frequency to estimate probabilities experimentally. Careers that apply probability theory are also listed.
CABT Math 8 - Fundamental Principle of Counting
This document provides an introduction to counting and probability. It defines key terms like sample space, outcome, and event. It discusses counting problems like determining the number of combinations that can be made from various clothing items. Examples are provided to illustrate how to use the fundamental principle of counting and product rules to solve counting problems involving multiple independent choices. The document also introduces basic probability concepts like computing the probability of an event occurring using the ratio of favorable outcomes to total possible outcomes. Examples demonstrate calculating probabilities for coin tosses, dice rolls, and drawing balls from containers.
12.7 probability and odds 1
The document provides lesson material on probability and odds, including definitions, examples and practice problems. It defines key terms like probability, complementary events, odds, and discusses how to calculate probabilities and odds for various scenarios. Practice problems ask students to calculate probabilities and odds based on given information, such as the likelihood of random outcomes or events.
PROBABILITY.pptx
Here are the probabilities of the compound events in the assignment:
1a) The probability of drawing an 8 or 16 is 2/20 = 0.1
1b) The probability of drawing a 5 or a number divisible by 3 is 11/20
1c) The probability of drawing an odd number or a number divisible by 3 is 17/20
1d) The probability of drawing a number divisible by 3 or divisible by 4 is 19/20
2) The probability of drawing a violet marble or a pink marble is 40/52
3) The probability that a randomly selected household has a rabbit or a dog is 1824/4820 + 720/4820 - 252/48
powerpoints probability.pptx
This document provides an overview of a lesson on sample spaces, subsets, and basic probability. It defines a sample space as the set of all possible outcomes of an event. It gives examples of sample spaces for tossing a coin, rolling a die, and drawing from a bag of marbles. It also discusses intersections and unions of sets, using Venn diagrams to visualize set relationships. The document concludes with examples of finding the probability of mutually exclusive and inclusive events using formulas and two-way tables.
12X1 T09 01 definitions & theory
The document defines key probability terms:
- Probability is the chance of an event occurring
- The sample space includes all possible outcomes
- Equally likely events have the same chance of occurring
- Mutually exclusive events cannot both occur simultaneously
- Non-mutually exclusive events can occur together
It also provides examples of calculating probabilities of dice rolls.
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L3 10 1
- 1. EQ: How are the terms of probability used correctly to describe an event? Course 3 10-1 Probability
- 2. Warm Up Write each fraction in simplest form. 1. 2. 3. 4. 8 64 Course 3 10-1 Probability 16 20 12 36 39 195 4 5 1 3 1 8 1 5
- 3. Vocabulary experiment trial outcome sample space event probability impossible certain Insert Lesson Title Here Course 3 10-1 Probability
- 6. 0 0.25 0.5 0.75 1 0% 25% 50% 75% 100% Never Happens about Always happens half the time happens 0 1 Course 3 10-1 Probability 1 4 1 2 3 4
- 7. Give the probability for each outcome. Example #1 The basketball team has a 70% chance of winning. The probability of winning is P (win) = 70% = 0.7. The probabilities must add to 1, so the probability of not winning is P (lose) = 1 – 0.7 = 0.3, or 30%. Course 3 10-1 Probability
- 8. Give the probability for each outcome. Example #2 Course 3 10-1 Probability Three of the eight sections of the spinner are labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P (1) = . 3 8
- 9. Give the probability for each outcome. With your partner – Example #3 Rolling a number cube. Course 3 10-1 Probability One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P (1) = . 1 6 Outcome 1 2 3 4 5 6 Probability One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P (2) = . 1 6
- 10. Check It Out: Example 1B Continued Course 3 10-1 Probability One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P (3) = . 1 6 One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 4 is P (4) = . 1 6 One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 5 is P (5) = . 1 6
- 11. Check It Out: Example 1B Continued Check The probabilities of all the outcomes must add to 1. Course 3 10-1 Probability One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 6 is P (6) = . 1 6 1 6 1 6 1 6 + + = 1 1 6 + 1 6 + 1 6 +
- 12. To find the probability of an event, add the probabilities of all the outcomes included in the event. Course 3 10-1 Probability
- 13. A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Example #4 What is the probability of guessing 3 or more correct? The event “three or more correct” consists of the outcomes 3, 4, and 5. P (3 or more correct) = 0.313 + 0.156 + 0.031 = 0.5, or 50%. Course 3 10-1 Probability
- 14. What is the probability of guessing fewer than 2 correct? The event “fewer than 2 correct” consists of the outcomes 0 and 1. P (fewer than 2 correct) = 0.031 + 0.156 = 0.187, or 18.7% Example #5 A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Course 3 10-1 Probability
- 15. What is the probability of passing the quiz (getting 4 or 5 correct) by guessing? The event “passing the quiz” consists of the outcomes 4 and 5. P (passing the quiz) = 0.156 + 0.031 = 0.187, or 18.7% Additional Example 2C: Finding Probabilities of Events A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Course 3 10-1 Probability
- 16. A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score. Check It Out: Example 2A What is the probability of guessing 2 or more correct? The event “two or more correct” consists of the outcomes 2, 3, 4, and 5. P (2 or more) = 0.313 + 0.313 + 0.156 + 0.031 = .813, or 81.3%. Course 3 10-1 Probability
- 17. Lesson Quiz Use the table to find the probability of each event. 1. 1 or 2 occurring 2. 3 not occurring 3. 2, 3, or 4 occurring 0.874 0.351 Insert Lesson Title Here 0.794 Course 3 10-1 Probability
- 18. Ticket Out: What is the difference between an outcome and an event? Course 3 10-1 Probability