Flipping three face cards before the joker
Question
A 14-card deck consists of one card of each rank (ace through king) plus a joker, shuffled. You turn cards over one by one. You win $100 if the king, queen and jack have all been revealed, but the game ends with nothing as soon as the joker appears. What is the most you should pay to play?
Short answer
$25. Only the relative order of the king, queen, jack and joker matters. You win exactly when the joker is last of those four, which has probability , so the expected payout is $25.
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Open the worked solutionLessons behind this question
- Counting and Combinatorics
- Matrix Algebra: Operations, Rules, and the Transpose
- Kernel, Image, and the Rank-Nullity Theorem
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