2006 AMC 10B Problems/Problem 21
Revision as of 15:04, 2 August 2006 by Xantos C. Guin (talk | contribs) (added link to previous and next problem)
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
.
Since the sum of the probabilities of rolling each number must equal 1:
So the probabilities of rolling a ,
,
,
,
, and
are
,
,
,
,
,
.
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.