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Interview prep / Brainteaser/Logic

Re-flipping only the heads until a uniform result

Question

Twenty-five fair coins are tossed together. Any coin that lands tails is set aside, and the coins that landed heads are tossed again. This repeats until either no coins remain or every coin in the latest toss lands heads. What is the chance the process finishes with every remaining coin showing heads?

Short answer

1/21/2. In any round the process stops only if the coins tossed that round are all heads or all tails. For the same number of coins those two outcomes have equal probability, so whenever it stops it is equally likely to be either way.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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