Question

If odds in favor of event \( E \) are \( a : b \), then \( P(E) = \).

• A. \( \frac{a}{a-b} \)
• B. \( \frac{a}{a+b} \)
• C. \( \frac{b}{a+b} \)
• D. \( \frac{b}{a-b} \)

Hint:

The odds in favor of an event are the ratio of favorable to unfavorable outcomes. The probability is the ratio of favorable outcomes to total outcomes.

Answer 1

The Correct Option is B

The odds in favor of an event \( E \) occurring are given as \( a : b \), meaning that for every \( a \) favorable outcomes, there are \( b \) unfavorable outcomes. The probability of event \( E \) is given by: \[ P(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{a}{a + b}. \] Thus, the correct answer is option (B) \( \frac{a}{a+b} \).