The two-headed coin

Among 1000 coins, one is two-headed and the rest are fair. You pick one at random and flip 10 heads in a row. What is the probability it is the two-headed coin? (to 3 decimals)

Show hints (2)+
  1. A fair coin gives 10 heads with probability 1/10241/1024.
  2. Apply Bayes' rule.

Answer

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0.506 (± 0.005)

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