The black and red die are rolled. The conditional probability of obtaining a sum greater than 9 given that the black die resulted in a 5 is :

$\frac{1}{3}$

The correct answer is option (1) → $\frac{1}{3}$

Given that black die already comes up with 5

we have 6 possibilities for red die 

only for 5, 6 on red die, the combined sum = 9

so probability = $\frac{2}{6}=\frac{1}{3}$