<s>[INST] Rolling two dice, what is the probability of getting 6 on either of them, but not both? Rolling two dice, what is the probability of getting 6 on one of them, but not both?
 [/INST] Total outcomes: $6^2 = 36$.
Allowed outcomes is the complementary of unallowed outcomes which can be split into "both dice < 6" ( case 1 ) "and" "not both dice = 6" ( case 2 ):
$6^2 - 5^2 - 1^2 = 36-25-1 = 10$. We can write this as a binary number matrix with the indices equal to the dice results:
$\left(\begin{array}{cccccc} 1&1&1&1&1&0\\1&1&1&1&1&0\\1&1&1&1&1&0\\1&1&1&1&1&0\\1&1&1&1&1&0\\0&0&0&0&0&2\end{array}\right)$ we see that the number of which are 0 is 10.
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