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> | |
Revision as of 14:36, 8 February 2023
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 
where 
and 
are relatively prime positive integers. Find 
