Transcript Management Science BUS 340

Management Science
BUS 340
Chapter 2
Problem 2-24
Presented by: Kelly Devilbiss
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
X
1
The Machos (3)
1
4
X
Kelly Devilbiss
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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
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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
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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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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
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