Suppose that there are three coins on a box. Two of the coins are normal (one side is heads, the other is tails). The third coin has two heads. You choose a coin at random from the bag and toss it four times. Each of the four times, the coin turns up heads. a. What is the probability that the coin you have chosen is the two-headed coin? b. How many consecutive “heads” you must have to be at least 95% sure that the coin you have chosen is the coin with two “heads”?

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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Suppose that there are three coins on a box. Two of the coins are normal (one side is heads, the other is tails). The third coin has two heads. You choose a coin at random from the bag and toss it four times. Each of the four times, the coin turns up heads.

a. What is the probability that the coin you have chosen is the two-headed coin?

b. How many consecutive “heads” you must have to be at least 95% sure that the coin you have chosen is the coin with two “heads”?

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