Solution: 2022 Winter Final - 13

Author: Michiel Smid

Question

Let $D_1,\ldots,D_5$ be the results of rolling five normal $6$-sided dice and let $X=D_1+D_2+D_3+D_4+D_5$. What is $\Pr(X\bmod 4 = 0)$?

(a)

$1/6$

(b)

$1/2$

(c)

$1/4$

(d)

$1/3$

(e)

$1/5$

Since each roll of a dice does not affect the results of the next roll, this means that each dice roll is an independent event.

The only results with a remainder of 0 when divided by 4 are 8, 12, 16, 20, 24, and 28.

You can brute force the solution, by calculating all the probabilities of those numbers, with the result being $\frac{1}{4}$.