2022 AIME II Problems/Problem 2
Problem
Azar, Carl, Jon, and Sergey are the four players left in a singles tennis tournament. They are randomly assigned opponents in the semifinal matches, and the winners of those matches play each other in the final match to determine the winner of the tournament. When Azar plays Carl, Azar will win the match with probability 
. When either Azar or Carl plays either Jon or Sergey, Azar or Carl will win the match with probability 
. Assume that outcomes of different matches are independent. The probability that Carl will win the tournament is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See Also
| 2022 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
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