A person takes at random one of the numbers 1, 2 or 3, with equal probability each of them, and then rolls a balanced die as many times as indicated by the chosen number. Finally, add up the results of the dice rolls. Find the probability that the number 2 was chosen given that the sum of the rolls of the die is 8.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 41E
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A person takes at random one of the numbers 1, 2 or 3, with equal probability each of them, and then rolls a balanced die as many times as indicated by the chosen number. Finally, add up the results of the dice rolls. Find the probability that the number 2 was chosen given that the sum of the rolls of the die is 8.

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