+25 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?
Enter your answer, in simplest fraction form.
+605 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 $\frac{14}{36}=\frac{7}{18}$.
+876 I think PIE would be faster, though this is very rigorous without a doubt.
+876 $\frac{\lfloor \frac{36}{4} \rfloor + \lfloor \frac{36}{6} \rfloor - \lfloor \frac{36}{24}\rfloor}{36}$
$\frac{14}{36}$
$\frac{7}{18}$
