2009 AIME I Problems/Problem 3
Problem
A coin that comes up heads with probability and tails with probability
independently on each flip is flipped eight times. Suppose the probability of three heads and five tails is equal to
of the probability of five heads and three tails. Let
, where
and
are relatively prime positive integers. Find
.
Solution
The probability of three heads and five tails is and the probability of five heads and three tails is
.
Therefore, the answer is .
Solution 2
We start as shown above. However, as we get to , we square root both sides to get
. Then, we have:
We get the same answer as above, .
~Jerry_Guo
Video Solution
~IceMatrix
See also
2009 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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