Difference between revisions of "2016 AIME I Problems/Problem 2"
Aleph null (talk | contribs) m (→Solution) |
(→Solution) |
||
Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
It is easier to think of the dice as <math>21</math> sided dice with <math>6</math> sixes, <math>5</math> fives, etc. Then there are <math>21^2=441</math> possible rolls. There are <math>2\cdot(1\cdot 6+2\cdot 5+3\cdot 4)=56</math> rolls that will result in a seven. The odds are therefore <math>\frac{56}{441}=\frac{8}{63}</math>. The answer is <math>8+63=\boxed{071}</math> | It is easier to think of the dice as <math>21</math> sided dice with <math>6</math> sixes, <math>5</math> fives, etc. Then there are <math>21^2=441</math> possible rolls. There are <math>2\cdot(1\cdot 6+2\cdot 5+3\cdot 4)=56</math> rolls that will result in a seven. The odds are therefore <math>\frac{56}{441}=\frac{8}{63}</math>. The answer is <math>8+63=\boxed{071}</math> | ||
+ | |||
+ | See also [[2006 AMC 12B Problems/Problem 17]] | ||
== See also == | == See also == | ||
{{AIME box|year=2016|n=I|num-b=1|num-a=3}} | {{AIME box|year=2016|n=I|num-b=1|num-a=3}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 22:09, 9 June 2016
Problem 2
Two dice appear to be normal dice with their faces numbered from to
, but each die is weighted so that the probability of rolling the number
is directly proportional to
. The probability of rolling a
with this pair of dice is
, where
and
are relatively prime positive integers. Find
.
Solution
It is easier to think of the dice as sided dice with
sixes,
fives, etc. Then there are
possible rolls. There are
rolls that will result in a seven. The odds are therefore
. The answer is
See also 2006 AMC 12B Problems/Problem 17
See also
2016 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.