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**Management Science BUS 340**

Chapter 2 Problem 2-24 Presented by: Kelly Devilbiss

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**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

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**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

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**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

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**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

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**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

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