Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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

1. 1/4

2. 3/4

3. 3/1

4. 1/3

The correct answer is: 3/4

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