2004 AMC 12B Problems/Problem 4
Contents
[hide]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 |
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 AMC 12 Problems and Solutions |
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