Management Science BUS 340

# Management Science BUS 340

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## Management Science BUS 340

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

2. Boston South Fifth Street Softball LeagueWin-Loss Record (past 5 years) Kelly Devilbiss

3. 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. Kelly Devilbiss

4. 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) 1.0 - .16 = 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 = .5 + .5 = 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? 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 Kelly Devilbiss

6. 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 = .5 + .5 = 1.0 P(Killers wins against the Mama’s Boys and the Machos) = 2/5 x 1/5 = .4 x .2 = .08 Kelly Devilbiss