Question: You have three coins in your pocket: Coin 1 is a fair coin that comes up heads with probability 1/2. Coin 2 is

You have three coins in your pocket:

• Coin 1 is a fair coin that comes up heads with probability 1/2.

• Coin 2 is a biased coin that comes up heads with probability 1/4.

• Coin 3 is a biased coin that comes up heads with probability 3/4.

Suppose you pick one of the coins uniformly at random and flip it three times. If you observe the sequence HHT (where H stands for heads and T stands for tails), what is the probability that you chose Coin 3?

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