Difference between revisions of "2006 AMC 10B Problems/Problem 21"
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[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
Revision as of 22:04, 7 September 2011
Problem
For a particular peculiar pair of dice, the probabilities of rolling 
, 
, 
, 
, 
, and 
, on each die are in the ratio 
. What is the probability of rolling a total of 
on the two dice?
Solution
Let 
be the probability of rolling a . The probabilities of rolling a
, , , , and are 
, 
, 
, 
, and 
, respectively.
The sum of the probabilities of rolling each number must equal 1, so
So the probabilities of rolling a , , , , , and are respectively 
, and 
.
The possible combinations of two rolls that total are: 
The probability of rolling a total of on the two dice is equal to the sum of the probabilities of rolling each combination.
See Also
| 2006 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
