Conditional probability · Coin flips · difficulty 4 of 5
Ten heads from a mystery coin
A coin comes out of a machine with an unknown probability of heads, equally likely to be any value between 0 and 1 (a uniform prior). It is flipped 10 times, independently, and lands heads 10 times. What is the probability that the next flip of the same coin lands heads?
Answer with a probability. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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