Playing a card game in which 2 52 card decks are combined to create the pile and from this pile each player is dealt 14 cards. One rule of the game is if any player is dealt 3 doubles (a double being a card with same suite and value) a re-shuffle is permitted. However if a player is accidentally dealt 15 cards and is found to have 3 doubles what is the probability that the 15th card completed the three doubles.
2026-03-28 04:52:20.1774673540
Card Game Probability, the 15th card
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If there are $15$ cards dealt with exactly three doubles
then there are $6$ cards of the $15$ which are in the doubles
so the probability one of these $6$ was the last of the $15$ to be dealt is $\dfrac6{15}$