3 coins

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Question: You have three coins. One always comes up heads, one always comes up tails, and one is just a regular coin (has equal change of heads or tails). If you pick one of the coins randomly and flip it twice and get heads twice, what is the chance of flipping heads again?

Answer: 90 percent. If you pick the heads coin the chance of getting the first 2 heads is 100 percent (4/4) and if you pick the fair coin the chance is 25 percent (1/4). So from this, the chance that it is the heads coin is 4/5 and the fair coin 1/5.

Then, if it is the heads coin you will definitely get heads (4/5). If you flip the fair coin it is 1/10 (1/5 * 1/2). Add the probabilities together: 4/5 + 1/10 = 9/10.

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