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 P A P not A 5

P A P Ac .

For instance, if P A 5 0.60, then P Ac 5 0.40 and the odds in favor of A are 0.60 0.40 5

6 4

5 3

2

, written as 3 to 2 or 3:2

(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 5 n

n 1 m

. Hint: Solve the equation n

m 5

P A 1  P A for P(A).

(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?

(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?