EXAMPLE 3.3.8

A jar contains a penny, a nickel, a dime, a quarter, and a half-dollar. Two coins are

randomly selected (without replacement) and their monetary sum is determined.

1. What is the probability that their monetary sum will be 55¢?

A. 1/25

B. 1/32

C. 1/9

D. 1/10

SOLUTION

A monetary sum is determined by which two of the five coins are selected, so the number of different outcomes (the number of different monetary sums) is C(5,2) = 10. There are 10 different outcomes possible. Of these 10 outcomes, exactly one of them is a sum of 55¢, so P(sum is 55¢) = 1/10

2. What is the probability that the monetary sum will be 48¢?

A. 1/10

B. 1/9

C. 1/32

D. 0

SOLUTION

There are 10 possible monetary sums. Of these ten possible outcomes, none of them is a sum of 48¢ (it's not possible to combine two of those coins and have them add up to 48¢), so P(sum is 48¢) = 0/10 = 0.