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

Two dice are rolled simultaneously - a black die and a red die.

Given that the black die shows 5, we need to find the probability that the sum is greater than 9.

Since the black die is fixed at 5, only the red die outcome matters.

The sum is: Black die + Red die = 5 + Red die

For the sum to be greater than 9:

$5 + \text{Red die} > 9$

$\text{Red die} > 4$

A standard die shows values 1, 2, 3, 4, 5, 6.

The red die must show a value greater than 4.

Favorable outcomes: Red die shows 5 or 6

Number of favorable outcomes = 2

Total possible outcomes for red die = 6

$\text{Probability} = \dfrac{\text{Favorable outcomes}}{\text{Total possible outcomes}}$

$\text{Probability} = \dfrac{2}{6}$

$\text{Probability} = \dfrac{1}{3}$

Therefore, the probability of obtaining a sum greater than 9, given that the black die shows 5, is $\dfrac{1}{3}$.