Answer
$\frac{3}{10}$
Work Step by Step
Let us define events A and B as
A: sum exceeds 8.
B: sum equals 10.
Then, A= {(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)},
B= {(4,6),(5,5),(6,4)} and
A$\cap$B= {(4,6),(5,5),(6,4)}.
$\implies$ P(A)=$\frac{10}{36}$ and $P(A\cap B)=\frac{3}{36}$.
Therefore, $P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{3/36}{10/36}=\frac{3}{10}$
