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

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Kelly Devilbiss2 Boston South Fifth Street Softball League Win-Loss Record (past 5 years) Winner (1)(2)(3) Mama’s Boys (1)X34 The Killers (2)2X1 The Machos (3)14X

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Kelly Devilbiss3 a.What is the probability that the Killers will win every game next year? 2/5 x 1/5 = 2/25 = 0.08 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 In the last five years, the Killers have beat the Machos 1 time.

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Kelly Devilbiss4 b.What is the probability that the Machos will win at least one game next year? 1/2 + 1/2 - (1/5 x 4/5) = 0.84 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

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Kelly Devilbiss5 c.What is the probability that the Mama’s Boys will win exactly one game next year? 4/6 x 4/6 = 16/36 = 0.44 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

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Kelly Devilbiss6 d.What is the probability that the Killers will win less than two games next year? 1/2 + 1/2 – (2/5 x 1/5) = 1.0 – 0.08 = 0.92 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

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