2006 AMC 10B Problems/Problem 21
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.
