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

1/3

The correct answer is Option (4) → 1/3

The black die shows $5$.

Sum > 9 ⇒ red die must show a number $r$ such that:

$5 + r > 9$

$r > 4$

Possible red die outcomes: $5,6$ → total $2$ outcomes.

Total possible outcomes for red die (given black = 5): $6$.

Required probability:

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

Probability = $\frac{1}{3}$.