One number from the set {1, 2, 3} is selected at random. Then a fair coin is flipped x times, where x equals the number that was chosen randomly from the set. What is the probability that 3 was chosen from the set given that (a) no heads were seen on any of the coin flips (b) exactly 1 head was seen on the coin flips (c) exactly 2 heads were seen on the coin flips (d) exactly 3 heads were seen on the coin flips?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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One number from the set {1, 2, 3} is selected at random. Then a fair coin is flipped x times,
where x equals the number that was chosen randomly from the set. What is the probability that 3
was chosen from the set given that (a) no heads were seen on any of the coin flips (b) exactly 1
head was seen on the coin flips (c) exactly 2 heads were seen on the coin flips (d) exactly 3 heads
were seen on the coin flips?

 

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