2023 AIME I Problems/Problem 6: Difference between revisions
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== Problem == | |||
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 15:34, 8 February 2023
Problem
Alice knows that 
red cards and 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 
where 
and 
are relatively prime positive integers. Find 
