Difference between revisions of "2023 AIME I Problems/Problem 6"
MRENTHUSIASM (talk | contribs) |
|||
Line 1: | Line 1: | ||
− | + | == 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 16:34, 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