Difference between revisions of "2006 AMC 10B Problems/Problem 21"
m (wikified) |
m (added link to previous and next problem) |
||
Line 26: | Line 26: | ||
== See Also == | == See Also == | ||
*[[2006 AMC 10B Problems]] | *[[2006 AMC 10B Problems]] | ||
+ | |||
+ | *[[2006 AMC 10B Problems/Problem 20|Previous Problem]] | ||
+ | |||
+ | *[[2006 AMC 10B Problems/Problem 22|Next Problem]] |
Revision as of 15:04, 2 August 2006
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.