155.The Coin With Two Heads
★★★conditional probabilityJane Street
A pocket holds two coins: one ordinary fair coin, and one trick coin with heads on both sides. You draw one at random and flip it, and it lands heads. What is the probability that the coin you drew has tails on its other side?
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The trick coin produces heads twice as often as the fair one does. Weight the two candidates by how likely each was to have produced what you saw.
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