Difference between revisions of "2002 AIME II Problems/Problem 12"
I like pie (talk | contribs) (Added problem, solution still needed) |
Talkinaway (talk | contribs) (changed a10 < .4 to a10 = .4, making the problem actually solvable!) |
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== Problem == | == Problem == | ||
− | 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} | + | 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} = .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 02:06, 16 December 2008
Problem
A basketball player has a constant probability of of making any given shot, independent of previous shots. Let be the ratio of shots made to shots attempted after shots. The probability that and for all such that is given to be where , , , and are primes, and , , and are positive integers. Find .
Solution
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See also
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 | ||
All AIME Problems and Solutions |