Difference between revisions of "1995 AIME Problems/Problem 15"
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== Problem == | == Problem == | ||
| + | Let <math>\displaystyle p_{}</math> be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that <math>\displaystyle p_{}</math> can be written in the form <math>\displaystyle m/n</math> where <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> are relatively prime positive integers, find <math>\displaystyle m+n</math>. | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1995_AIME_Problems/Problem_14|Previous Problem]] | ||
* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
Revision as of 01:35, 22 January 2007
Problem
Let 
be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that can be written in the form 
where 
and 
are relatively prime positive integers, find 
.
