1. Management Science BUS 340
Chapter 2 Problem 2-24
Presented by: Kelly Devilbiss

2. Boston South Fifth Street Softball League Win-Loss Record (past 5 years)
Winner
(1)
(2)
(3)
Mama’s Boys (1) X 3 4
The Killers (2) 2 1
The Machos (3)
Kelly Devilbiss

3. a. What is the probability that the Killers will win every game next year?
Solution: Joint Probability: P(AB) = P(A) x P(B)
P(Killers beating the Mama’s Boys) = 2/5
In the last five years, the Killers have beat the
Mama’s Boys 2 times.
P(Killers beating the Machos) = 1/5
Machos 1 time.
Kelly Devilbiss

4. b. What is the probability that the Machos will win at least one game next year?
Solution: Law of Addition for events that are not mutually exclusive [P(A or B) = P(A) + P(B) – P(A and B)]
P(Machos will beat the Mama’s Boys or the Killers) =
½ + ½ = = 1.0
P(Machos will beat the Mama’s Boys and the Killers) =
1/5 x 4/5 = .2 x .8 = .16
Kelly Devilbiss

5. c. What is the probability that the Mama’s Boys will win exactly one game next year?
Solution: Joint Probability for Independent Events
P(AB) = P(A) x P(B)
P(Mama’s Boys will win against the Killers) = 4/6
but
P(Mama’s Boys will not win against the Machos) = 4/6
Kelly Devilbiss

6. d. What is the probability that the Killers will win less than two games next year?
Solution: Law of Addition for events that are not mutually exclusive [P(A or B) = P(A) + P(B) – P(A and B)]
P(Killers will against the Mama’s Boys or the Machos) =
½ + ½ = = 1.0
P(Killers wins against the Mama’s Boys
and the Machos) = 2/5 x 1/5 = .4 x .2 = .08
Kelly Devilbiss