Difference between revisions of "2016 AIME I Problems/Problem 2"
(→Solution) |
(→See also) |
||
Line 5: | Line 5: | ||
== See also == | == See also == | ||
− | {{AIME box|year=2016|n=I|num-b= | + | {{AIME box|year=2016|n=I|num-b=1|num-a=3}} |
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 16:54, 4 March 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
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.