Difference between revisions of "2021 AIME I Problems/Problem 1"
Sugar rush (talk | contribs) |
Sugar rush (talk | contribs) |
||
| Line 7: | Line 7: | ||
==See also== | ==See also== | ||
{{AIME box|year=2021|n=I|before=First problem|num-a=2}} | {{AIME box|year=2021|n=I|before=First problem|num-a=2}} | ||
| + | |||
| + | [[Category:Introductory Combinatorics Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:57, 11 March 2021
Problem
Zou and Chou are practicing their 100-meter sprints by running 
races against each other. Zou wins the first race, and after that, the probability that one of them wins a race is 
if they won the previous race but only 
if they lost the previous race. The probability that Zou will win exactly 
of the races is 
, where 
and 
are relatively prime positive integers. What is 
?
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
