The Green Bay Packers and Chicago Bears are playing a charity benefit game. It i
ID: 3309852 • Letter: T
Question
The Green Bay Packers and Chicago Bears are playing a charity benefit game. It is 3rd down with 4 yards to go for the Packers on their own 45 yard line. Based on previous performances by the Packers, the next play will see one of the following occurrences, with probabilities indicated below:
· Pass incomplete 0.25
· Pass complete for a first down 0.15
· Pass complete with no first down 0.05
· Pass is intercepted 0.03
· Run is attempted and a first down results 0.20
· Busted play, quarterback is sacked 0.25
· Whistle is blown before the play 0.02
· Ball is fumbled on the snap and the Bears recover 0.05
Find the following probabilities for the next play: (5 points each)
a) Packers get a first down
b) Packers attempt a pass play
c) Packers pass the ball and get a first down
d) Packers turn the ball over
e) Is this question transferrable to business? If so, how?
Explanation / Answer
(a) P(packers get a first down) : P(pass complete for a first down)+P(Run is attempted and a first down results)
= 0.20+0.15 = 0.35
(b) P(attempt a pass play) : P(Pass incomplete)+ P(Pass complete for a first down)+P(Pass complete for a no down)+P(Pass is intercepted)
= 0.25+0.15+0.05+0.03 = 0.48
(c) P(Packers pass the ball and get a first down) = P(Pass complete for a first down)/P(attempt a pass play)
= 0.15/0.48 = 0.3125
(d) P(Packers turn the ball over) : P(Busted play, quarterback is sacked)+P(Ball is fumbled on the snap and the Bears recover)+P(Whistle is blown before the play) = 0.25+0.02+0.05 = 0.32
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