2004 AMC 12B Problems/Problem 4
Problem
An integer , with , is to be chosen. If all choices are equally likely, what is the probability that at least one digit of is a 7?
Solution
The digit can be either the tens digit (: possibilities), or the ones digit (: possibilities), but we counted the number twice. This means that out of the two-digit numbers, have at least one digit equal to . Therefore the probability is .
Solution 2
By complementary counting, we count the numbers that do not contain a , then subtract from the total. There is a probability of choosing a number that does NOT contain a . Subtract this from and simplify yields .
Video Solution 1
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See Also
2004 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 3 |
Followed by Problem 5 |
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All AMC 12 Problems and Solutions |
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