Question

determine whether the following statement is true or false. the odds against e can always be found by reversing the ratio representing the odds in favor of e. the statement is because the odds in favor of e are found by taking the probability that and dividing by the probability that and the odds against e are found by taking the probability that and dividing by the probability that

Explanation:

Step1: Recall the formula for odds in favor

The odds in favor of an event \(E\) is given by \(\frac{P(E)}{P(\text{not }E)}\).

Step2: Recall the formula for odds against

The odds against an event \(E\) is given by \(\frac{P(\text{not }E)}{P(E)}\).

Answer:

The statement is true because the odds in favor of \(E\) are found by taking the probability that \(E\) occurs and dividing by the probability that \(E\) does not occur and the odds against \(E\) are found by taking the probability that \(E\) does not occur and dividing by the probability that \(E\) occurs.