Two fair dice are rolled. What is the probability that Their sum is $10$, given that the first roll is an even number

Question

For sure I am missing something but I am confused.

My reasoning for the problem is: When the first dice is even, the only numbers that sum $10$ are $4$ and $6$, so the result should be $2/6$.

It seems that this answer is incorrect, so i must be reasoning wrong. Any tip to put me ontrack?

Answer 1

Of the $36$ possible outcomes of a roll of two dice, $18$ correspond to the first die being even. Of those $18$, only two result in a sum of $10$, namely $(4,6)$ and $(6,4)$. Thus, your desired probability should be $\frac{2}{18}=\frac19$.