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HMMT 2007 C3

  • Combinatorics
  • Answer

Jack, Jill, and John play a game in which each randomly picks and then replaces a card from a standard 52 card deck, until a spades card is drawn. What is the probability that Jill draws the spade? (Jack, Jill, and John draw in that order, and the game repeats if no spade is drawn.)

Dataset text NuminaMath olympiads. Quoted with source.

Also HMMT 2007 E7.

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\frac{12}{37}

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