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Question: 2022 Winter Final - 13

Author: Michiel Smid
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)
$1/3$
(b)
$1/4$
(c)
$1/6$
(d)
$1/2$
(e)
$1/5$