Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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If the odds against an event are 3:1, what is the probability of the event not occurring?

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To understand the relationship between odds and probability, we first need to break down what it means for the odds against an event to be 3:1. This indicates that there are 3 unfavorable outcomes for every 1 favorable outcome.

When calculating the total outcomes based on these odds, you add together the favorable and unfavorable outcomes. Since there are 3 unfavorable outcomes and 1 favorable outcome, the total number of outcomes is 3 + 1 = 4.

The probability of an event occurring is given by the formula:

\[

P(\text{event occurring}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{4}.

\]

Conversely, the probability of an event not occurring is calculated by subtracting the probability of the event occurring from 1:

\[

P(\text{event not occurring}) = 1 - P(\text{event occurring}) = 1 - \frac{1}{4} = \frac{3}{4}.

\]

Thus, with odds of 3:1 against the event, the probability of the event not occurring correctly results in \(\frac{3}{4}\). This probability reflects that there are significantly more

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