Question

fill in the blank so that the resulting statement is true.
if the odds in favor of event e are a to b, then the probability of the event, ( p(e) ) is given by the formula ( p(e) ) =
if the odds in favor of event e are a to b, then the probability of the event, ( p(e) ) is given by the formula ( p(e) ) =

Explanation:

Step1: Understand the concept of odds

Odds in favor of an event \(E\) being \(a\) to \(b\) means there are \(a\) favorable outcomes and \(b\) unfavorable outcomes.

Step2: Calculate the total number of outcomes

The total number of outcomes is the sum of favorable and unfavorable outcomes, which is \(a + b\).

Step3: Use the probability formula

Probability \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P(E)=\frac{a}{a + b}\).

Answer:

\(\frac{a}{a + b}\)