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 (\frac{8}{13})
(type an integer or a simplified fraction.)

(b) 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 against

If the odds against an event \( E \) are \( a \) to \( b \), then the probability of \( E \) occurring is \( \frac{b}{a + b} \). Here, the odds against \( E \) are 14 to 9, so \( a = 14 \) and \( b = 9 \).

Step2: Calculate the probability

Substitute \( a = 14 \) and \( b = 9 \) into the formula: \( \frac{9}{14 + 9}=\frac{9}{23} \).

Answer:

\(\frac{9}{23}\)