Question

in each case, find the probability of an event e having the given odds. (a) the odds in favor of e are 5 to 7 (b) the odds against e are 8 to 19. (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 \( P(E) \) when the odds in favor of \( E \) are \( a \) to \( b \) is \( P(E)=\frac{a}{a + b} \).
Here, \( a = 5 \) and \( b = 7 \).

Step2: Substitute the values into the formula

Substitute \( a = 5 \) and \( b = 7 \) into the formula \( P(E)=\frac{a}{a + b} \).
We get \( P(E)=\frac{5}{5 + 7}=\frac{5}{12} \).

Answer:

\(\frac{5}{12}\)