# Odds and Probability. 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.

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Odds and Probability

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.

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

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

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:

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.

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?

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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