Difference between revisions of "2001 AIME II Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | Club Truncator is in a soccer league with six other teams, each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win, lose, or tie are each <math>\frac {1}{3}</math>. The probability that Club Truncator will finish the season with more wins than losses is <math>\frac {m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=II|num-b=10|num-a=12}} | |
Revision as of 23:44, 19 November 2007
Problem
Club Truncator is in a soccer league with six other teams, each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win, lose, or tie are each 
. The probability that Club Truncator will finish the season with more wins than losses is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
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See also
| 2001 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
