We can calculate odds if we know the probability. But we can also go the other w

Question

We can calculate odds if we know the probability. But we can also go the other way. Suppose the odds in favor of an event are 3 to 2. We can interpret this as saying that there are three (equally likely) favorable outcomes and two unfavorable ones. That is a total of five outcomes. So the probability of the event occurring is 3/5. In general, if the odds in favor are p to q, then the probability is p/(p + q). Suppose the odds against an event are 2 to 1.

What is the probability that the event will occur? (Give the probability as a decimal. Round your answer to three decimal places.)

What is the probability that the event will not occur? (Give the probability as a decimal. Round your answer to three decimal places.)

Explanation / Answer

Suppose the odds against an event are 2 to 1.

1. What is the probability that the event will occur?

probability of even will occuring = 2 / (2+1) = 2/3 = 0.667

2. What is the probability that the event will not occur

probability of even not occuring = 1 / (2+1) = 1/3 = 0.333

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