1997 AJHSME Problems/Problem 20
Contents
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 that land face-up exceeds 36 is
Solution
There are combinations to examine.
If one die is , then even with an on the other die, no combinations will work.
If one die is , then even with an on the other die, no combinations will work.
If one die is , then even with an on the other die, no combinations will work.
If one die is , then even with an on the other die, no combinations will work.
If one die is , then the other die must be an to have a product over . Thus, works.
If one die is , then the other die must be either or to have a product over . Thus, and both work.
If one die is , then the other die can be or to have a product over . Thus, , , and all work.
If one die is , then the other die can be or to have a product over . Thus, and work.
There are a total of combinations that work out of a total of possibilities.
Thus, the answer is , and the answer is
But this may be slightly complicated, so you can also do solution 2 (scroll to bottom).
Solution 2
Make a chart with all products. 10 work out of 64. SImplify for 5/32 or .
See also
1997 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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