2002 AMC 12B Problems/Problem 16
Problem
Juan rolls a fair regular octahedral die marked with the numbers through
. Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3?
Solution
Solution 1
On both dice, only the faces with the numbers are divisible by
. Let
be the probability that Juan rolls a
or a
, and
that Amal does. By the Principle of Inclusion-Exclusion,
Alternatively, the probability that Juan rolls a multiple of is
, and the probability that Juan does not roll a multiple of
but Amal does is
. Thus the total probability is
.
Solution 2
The probability that neither Juan nor Amal rolls a multiple of is
; by the complement principle, the probability that at least one does is
.
See also
2002 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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All AMC 12 Problems and Solutions |