A box contains 1 fair coin and 1 2-Headed coin. A coin is drawn and flipped...

A box contains 1 fair coin and 1 2-Headed coin. A coin is drawn and flipped several times.

(a) The first flip results in Heads. What is the probability that the coin is fair?

(b) 3 flips result in all Heads. What is the probability that the coin is fair?

(c) 5 flips result in all Heads. What is the probability that the coin is fair?

(d) How many flips of all Heads are required to know with 99.9% accuracy that the coin is not fair?

Expert Solution

When we flip a fair coin, the probability of getting head is 1/2 and getting a tail is 1/2 since it is equally likely that we can getting head or tail in a trial of flipping a fair coin. If the coin is unfair than we won't have the same probability for each of two events mentioned above. Here we have used Bayes theorem for probability. So solution is as follows.

milcah answered 2 months ago

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