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.

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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:

$$5 + \text{Red die} > 9$$5+Red die>9

$$\text{Red die} > 4$$Red die>4

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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

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

$$\text{Probability} = \dfrac{2}{6}$$Probability=62​

$$\text{Probability} = \dfrac{1}{3}$$Probability=31​

Therefore, the probability of obtaining a sum greater than 9, given that the black die shows 5, is $\dfrac{1}{3}$31​.