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Probability and Odds

Probability and Odds. I. Finding the Probability of an Event. The probability of an event is a measure of the likelihood that the event will occur. The different possible results are called outcomes . An event consists of a collection of outcomes.

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Probability and Odds

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  1. Probability and Odds

  2. I. Finding the Probability of an Event • The probability of an event is a measure of the likelihood that the event will occur. • The different possible results are called outcomes. • An event consists of a collection of outcomes. • The outcomes for an event you wish to have happen are called favorable outcomes. Theoretical probability P = Number of favorable outcomes Total number of outcomes

  3. A. Finding the Probability of an Event • You toss two coins. What is the probability P that both are heads? Solution: There are four possible outcomes that are equally likely. P = Number of favorable outcomes = 1 = 0.25 Total number of outcomes 4

  4. Finding the Probability of an Event • An algebra class has 17 boys and 16 girls. One student is chosen at random from the class. What is the probability P that the student is a girl? Solution: Because the student is chosen at random, it is equally likely that any of the 33 students will be chosen. Let “number of girls” be the favorable outcome. Let “number of students” be the total number of outcomes. P = __Number of girls___ = 16 ≈ 0.485 Number of Students 33

  5. Finding the Probability of an Event • Experimental probability is a type of probability that is based on repetitions of an actual experiment and is calculated by the following rule: Experimental Probability P = Number of favorable outcomes observed Total Number of trials

  6. B. Using a Survey to find a Probability Surveys are a type of experiment. Probabilities based on the outcomes of a survey can be used to make predictions. • There was a poll of 500 teens asking “Where would you like to live?” The results were: 155 – Large city 70 – Rural/Ranch 90 – Small town 85 – Wilderness area 100 – Suburbs If you were to ask a randomly chosen teen this question, what is the probability that the teen would say large city? Solution: Let “choosing large city” be the favorable outcome. Let “number surveyed” be the total number of trials. Experimental Probability P = Number choosing large city = 155 = 0.31 Number Surveyed 500

  7. II. Finding the Odds of an Event • When all outcomes are equally likely, the odds that an event will occur are given by the formula below. Odds = __Number of favorable outcomes__ Number of unfavorable outcomes

  8. A. Finding the Odds of an Event You randomly choose an integer from 0 through 9. What are the odds that the integer is 4 or more? Solution: There are 6 favorable outcomes: 4, 5, 6, 7, 8, and 9. There are 4 unfavorable outcomes: 0, 1, 2, and 3. Odds = __Number of favorable outcomes_ = 6 = 3 Number of unfavorable outcomes 4 2 The odds that the integer is 4 or more are 3 to 2.

  9. Finding the Odds of an Event • If you know the probability that an event will occur, then you can find the odds by using the following rule: Odds = ___Probability event will occur__ = ____Probability event will occur__ Probability event will not occur 1 – (Probability event will occur)

  10. B. Finding Odds from Probability The probability that a randomly chosen household has a cat is 0.27. What are the odds that a household has a cat? Odds = __Probability event will occur__ 1 – (Probability event will occur) = __0.27__ = _ 0.27_ = 27 1 – 0.27 1 – 0.27 43 The odds are 27 to 73 that a randomly chosen household has a cat.

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