Difference between revisions of "2002 AIME II Problems/Problem 12"

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

Revision as of 13:55, 19 April 2008

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 $a_{10}\le.4$ 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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See also

2002 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
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