Problem:
A pair of 8-sided dice have sides numbered 1 through 8. Each side has the same probability (chance) of landing face up. The probability that the product of the two numbers on the sides that land face-up exceeds 36 is
Answer Choices:
A. 325
B. 6411
C. 163
D. 41
E. 21
Solution:
There are 64 equally likely possibilities for the numbers on the two dice. Of these, only (5,8), (6,7), (6,8), (7,6), (7,7), (7,8), (8,5), (8,6), (8,7), and (8,8) give products exceeding 36, so the probability of this occurring is 6410=325.
OR
Make a table for the sample space:
x1234567811234567822468101214163369121518212444812162024283255101520253035(40)661218243036(42)(48)7714212835(42)(49)(56)88162432(40)(48)(56)(64)
The ten circled products exceed 36 so the probability of this occurring is 6410 or 325.
Answer: A.
The problems on this page are the property of the MAA's American Mathematics Competitions