2002 AIME II Problems/Problem 12

Problem

A basketball player has a constant probability of $.4$ of making any given shot, independent of previous shots. Let $a_n$ be the ratio of shots made to shots attempted after $n$ shots. The probability that $a_{10} = .4$ and $a_n\le.4$ for all $n$ such that $1\le n\le9$ is given to be $p^aq^br/\left(s^c\right)$ where $p$ , $q$ , $r$ , and $s$ are primes, and $a$ , $b$ , and $c$ are positive integers. Find $\left(p+q+r+s\right)\left(a+b+c\right)$ .

Solution

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2002 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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2002 AIME II Problems/Problem 12

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