Difference between revisions of "1993 AIME Problems/Problem 11"
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== Problem == | == Problem == | ||
+ | Alfred and Bonnie play a game in which they take turns tossing a fair coin. The winner of a game is the first person to obtain a head. Alfred and Bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. Suppose that Alfred goes first in the first game, and that the probability that he wins the sixth game is <math>m/n\,</math>, where <math>m\,</math> and <math>n\,</math> are relatively prime positive integers. What are the last three digits of <math>m+n\,</math>? | ||
== Solution == | == Solution == | ||
+ | {{solution}} | ||
== See also == | == See also == | ||
− | + | {{AIME box|year=1993|num-b=10|num-a=12}} |
Revision as of 23:19, 25 March 2007
Problem
Alfred and Bonnie play a game in which they take turns tossing a fair coin. The winner of a game is the first person to obtain a head. Alfred and Bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. Suppose that Alfred goes first in the first game, and that the probability that he wins the sixth game is , where and are relatively prime positive integers. What are the last three digits of ?
Solution
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See also
1993 AIME (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 |