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 | ||
