Chapter 4.1, 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 $\frac{P(A)}{P(notA)}=\frac{P(A)}{P(A^c)}.$

For instance, if P(A) = 0.60, then P(A^c) = 0.40 and the odds in favor of A are

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

1. (a) 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 $\frac{n}{m}=\frac{P(A)}{1-P(A)}$ for P(A).
2. (b) 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?
3. (c) 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?