2010 AMC 10B Problems/Problem 18
Problem
Positive integers , , and are randomly and independently selected with replacement from the set . What is the probability that is divisible by ?
Solution
First we factor as , so in order for the number to be divisible by 3, either is divisible by , or is divisible by .
We see that is divisible by with probability . We only need to calculate the probability that is divisible by .
We need or . Using some modular arithmetic, and or and . The both cases happen with probability so the total probability is .
Then the answer is or .
See Also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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