Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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When calculating odds against an event B, which formula is used?

P(B) / (1 - P(B))
(1 - P(B)) / P(B)
P(A) / P(B)
1 - P(B)

The correct answer is: (1 - P(B)) / P(B)

To determine the odds against an event B, the appropriate formula is given by the ratio of the probability of the event not occurring, which is (1 - P(B)), to the probability of the event occurring, which is P(B). Therefore, the formula to calculate odds against event B is (1 - P(B)) / P(B). This formula effectively highlights the relationship between the likelihood of the event failing to occur versus it occurring. In other words, it tells you how many times you would expect the event to fail for every time you would expect it to happen. This is particularly useful when assessing risks or making decisions based on probability. Understanding this concept is essential for evaluating situations in a variety of settings, such as finance, gambling, and scientific research, where the odds against an event can influence decision-making processes.