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Difference between revisions of "2023 AIME I Problems/Problem 6"
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Unofficial problem statement: Mary knows that a deck has 3 red cards and 3 black cards which will be revealed to her one at a time in random order. Before each card is revealed to her, she has to guess the color of the next card. If she plays optimally, the expected number of cards she guesses correctly can be written as <math>\frac{m}{n},</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n.</math>
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== Problem ==
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Alice knows that <math>3</math> red cards and <math>3</math> black cards will be revealed to her one at a time in random order. Before each card is revealed, Alice must guess its color. If Alice plays optimally, the expected number of cards she will guess correctly is <math>\frac{m}{n},</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n.</math>

Revision as of 16:34, 8 February 2023

Problem

Alice knows that $3$ red cards and $3$ black cards will be revealed to her one at a time in random order. Before each card is revealed, Alice must guess its color. If Alice plays optimally, the expected number of cards she will guess correctly is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$

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