A die is rolled 8 times. given that there were 3 sixes in the 8 rolls, what is the probability that there were 2 sixes in the first five rolls

Answer: 15/28

Suppose the following:

event A: the event that there were 3 sixes in the 8 roles,

event B: the event that there were 2 sixes in the first 5 roles.

Then the conditional probability to find is P (B|A) = P (A∩B) / P (A).

P (A) = C (3,8) * (1/6) ^3 * (5/6) ^5,

P (A∩B) = C (2,5) * (1/6) ^2 * (5/6) ^3*C (1,3) * (1/6) * (1/6) ^2

∴P (B|A) = 15/28