Question

in each case, find the probability of an event e having the given odds. (a) the odds in favor of e are 8 to 5. (b) the odds against e are 14 to 9. (c) the odds in favor of e are the same as the odds against e. (a) the probability of an event e occurring is \\(\square\\) (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for probability from odds in favor

The formula for the probability \( P(E) \) of an event \( E \) when the odds in favor of \( E \) are \( a \) to \( b \) is \( P(E)=\frac{a}{a + b} \).

Step2: Apply the formula to the given odds

Here, the odds in favor of \( E \) are 8 to 5, so \( a = 8 \) and \( b = 5 \).
Substitute these values into the formula: \( P(E)=\frac{8}{8 + 5}=\frac{8}{13} \).

Answer:

\(\frac{8}{13}\)