2008 AMC 10B Problems/Problem 20
Problem
The faces of a cubical die are marked with the numbers , , , , , and . The faces of another die are marked with the numbers , , , , , and . What is the probability that the sum of the top two numbers will be , , or ?
Solution
Solution 1
The easiest way is to write a table of all possible outcomes, do the sums, and count good outcomes.
1 3 4 5 6 8 ------------------ 1 | 2 4 5 6 7 9 2 | 3 5 6 7 8 10 2 | 3 5 6 7 8 10 3 | 4 6 7 8 9 11 3 | 4 6 7 8 9 11 4 | 5 7 8 9 10 12
We see that out of possible outcomes give the sum of , the sum of , and the sum of , hence the resulting probability is .
Solution 2
Each die is equally likely to roll odd or even, so the probability of an odd sum is .
So we can find the probability of rolling or instead and just subtract that from , which seems easier. Without writing out a table, we can see that there are two ways to make , and two ways to make , for a probability of .
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See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AMC 10 Problems and Solutions |
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