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Odds and Probability

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In many instances, the probability of an event is expressed as odds. We will learn how to find the odds for an event, given the probability of the event. We will also discuss how to find the probability of an event, given the odds for the event.

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Definition If the probability of an event E is p(E), then the odds for the event are defined as the ratio Odds are usually expressed as ratios of whole numbers. Odds are denoted by a/b or a : b Both are read: a to b

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Example #1 If the probability that it snows on July 4 is 0.2, what are the odds for that event?

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From Odds to Probability If the odds for an event E are a/b, then the probability of E can be found by using the formula:

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Example #2 The odds for a Democratic victory in the next Presidential election are 5 to 7. What is the probability that a Democratic victory will occur? We conclude that the probability that a Democratic victory will occur is 5/12, i.e. about 0.42.

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Example #3 Two fair dice are thrown. What are the chances of obtaining a sum of 10? What are the odds of obtaining a sum of 7?

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Example #4 In a beauty contest, the odds that your girlfriend will win are 2 to 3 and the odds that your ex-girlfriend will win are 1 to 2. Find the odds that neither one of them will win, assuming a tie is not possible.

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