Difference between revisions of "2021 Fall AMC 12B Problems/Problem 11"
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==Problem 11== | ==Problem 11== | ||
Una rolls <math>6</math> standard <math>6</math>-sided dice simultaneously and calculates the product of the <math>6{ }</math> numbers obtained. What is the probability that the product is divisible by <math>4?</math> | Una rolls <math>6</math> standard <math>6</math>-sided dice simultaneously and calculates the product of the <math>6{ }</math> numbers obtained. What is the probability that the product is divisible by <math>4?</math> |
Revision as of 00:34, 24 November 2021
- The following problem is from both the 2021 Fall AMC 10B #14 and 2021 Fall AMC 12B #11, so both problems redirect to this page.
Problem 11
Una rolls standard -sided dice simultaneously and calculates the product of the numbers obtained. What is the probability that the product is divisible by
Solution
We will first find the probability that the product is not divisible by . We have cases.
Case 1: The product is not divisible by .
We need every number to be odd, and since the chance we roll an odd number is our probability is
Case 2: The product is divisible by , but not by .
We need numbers to be odd, and one to be divisible by , but not by . There is a chance that an odd number is rolled, a chance that we roll a number satisfying the second condition (only and work), and ways to choose the order in which the even number appears.
Our probability is
Therefore, the probability the product is not divisible by is .
Our answer is .
~kingofpineapplz
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 10 Problems and Solutions |
2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
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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