Conditional Dice Probability

P(B|A) with dice examples

P(Sum greater than 8 | First Die is 5)

Question

You roll two dice. Given that the first die shows a 5, what is the probability that the sum of both dice is greater than 8?

Let A = "first die shows 5"

Let B = "sum greater than 8"

We want P(B|A)

Given first die = 5, second die can be 1-6:

Outcomes where sum greater than 8:

Sum = 9

Sum = 10

Sum = 11

Answer

With first die = 5, we need second die greater than or equal to 4 for sum greater than 8:

3 out of 6 possible second die values work, giving us 50%.