Difference between revisions of "2004 AMC 12B Problems/Problem 4"
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== Solution 2 == | == Solution 2 == | ||
By complementary counting, we count the numbers that do not contain a <math>7</math>, then subtract from the total. There is a <math>\frac{8}{9}\cdot\frac{9}{10}</math> probability of choosing a number that does NOT contain a <math>7</math>. Subtract this from <math>1</math> and simplify yields <math>1 - \frac{8}{9}\cdot\frac{9}{10} = \frac{90}{90} - \frac{72}{90} = \frac{18}{90} = \frac{1}{5}</math>. | By complementary counting, we count the numbers that do not contain a <math>7</math>, then subtract from the total. There is a <math>\frac{8}{9}\cdot\frac{9}{10}</math> probability of choosing a number that does NOT contain a <math>7</math>. Subtract this from <math>1</math> and simplify yields <math>1 - \frac{8}{9}\cdot\frac{9}{10} = \frac{90}{90} - \frac{72}{90} = \frac{18}{90} = \frac{1}{5}</math>. | ||
+ | |||
+ | == Video Solution 1== | ||
+ | https://youtu.be/s1771tqX32k | ||
+ | |||
+ | ~Education, the Study of Everything | ||
== See Also == | == See Also == |
Latest revision as of 19:22, 22 October 2022
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
~Education, the Study of Everything
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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