Chapter 5.1, Problem 21P

Expand Your Knowledge: Odds in Favor Sometimes probability statements are expressed in terms of odds.

The odds in favor of an event A are the ratio $\frac{P(A)}{P(notA)}=\frac{P(A)}{P(A^e)}$.

For instance, if $P\left(A\right)=0.60$, then $P\left(A^e\right)=0.40$ and the odds in favor of A are

$\begin{array}{l}\frac{0.60}{0.40}=\frac{6}{4}=\frac{3}{2}\\ \end{array}$, written as 3 to 2 or 3:2

Show that if we are given the odds in favor of event A as n:m, the probability of event A is given by $P(A)=\frac{n}{n+m}$, Hint: Solve the equation $\frac{n}{m}=\frac{P(A)}{1-P(A)}\text{ for }P(A)$.

A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 2 to 15. What is the probability of a successful call?

A sports announcer says that the odds a basketball player will make a free throw shot are 3 to 5. What is the probability the player will make the shot?