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# Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6.

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Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6.

What is the probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4?

Jul 28, 2021

#1
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The sum can be $4,6,8,12$. Some casework:

4 can be written as $2+2, 1+3, 3+1$

6 can be written as $1+5, 5+1, 4+2, 2+4, 3+3$

8 can be written as $2+6, 6+2, 3+5, 5+3, 4+4$

12 can be written as $6+6$

The total number of ways is $14$. There are $36$ possibilities. The answer is $\frac{14}{36}=\frac{7}{18}$.

Jul 28, 2021
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I think PIE would be faster, though this is very rigorous without a doubt.

MathProblemSolver101  Jul 28, 2021
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$\frac{\lfloor \frac{36}{4} \rfloor + \lfloor \frac{36}{6} \rfloor - \lfloor \frac{36}{24}\rfloor}{36}$

$\frac{14}{36}$

$\frac{7}{18}$

Jul 28, 2021