A penalty shoot-out in a game of hockey requires each of two players to take a penalty hit to try to score a goal. In a simple model, each player has a probability of 0.8 of scoring a goal, and independence is assumed. Calculate the probability that exactly one goal is scored from the two hits. In an alternative method, the probability of the second player scoring is reduced to 0.7 if the first player does not score. Draw a tree diagram to illustrate all the possible outcomes for the events. Calculate the probability that the second player has scored, given that only one goal is scored.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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5. A penalty shoot-out in a game of hockey requires each of two players to take a
penalty hit to try to score a goal. In a simple model, each player has a probability
of 0.8 of scoring a goal, and independence is assumed. Calculate the probability
that exactly one goal is scored from the two hits.
In an alternative method, the probability of the second player scoring is reduced
to 0.7 if the first player does not score. Draw a tree diagram to illustrate all the
possible outcomes for the events. Calculate the probability that the second
player has scored, given that only one goal is scored.
Transcribed Image Text:5. A penalty shoot-out in a game of hockey requires each of two players to take a penalty hit to try to score a goal. In a simple model, each player has a probability of 0.8 of scoring a goal, and independence is assumed. Calculate the probability that exactly one goal is scored from the two hits. In an alternative method, the probability of the second player scoring is reduced to 0.7 if the first player does not score. Draw a tree diagram to illustrate all the possible outcomes for the events. Calculate the probability that the second player has scored, given that only one goal is scored.
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