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

The odds in favor of an event A The odds in favor of an event Anaarree tthhee rraattiioo

( )

( )

( )

( )

.

P A P not A P A P Ac 5

The odds in favor of an event An are the ratio

( ( )

( )

.

P P P A P Ac 5

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 6

4 3

2 3 2 3 2

.

.

5 5 , written as to or : .

(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 n

n m 5

1

( ) . Hint: Solve the equation n

m P A P A 5

2

( )

1 ( )

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?

AppendixLO1