A die is thrown three times. Events A and B are defined as follows:

A: 4 on the third throw; B: 6 on the first and 5 on the second throw.

Find the probability of A given that B has already occurred.

There are 6 × 6 × 6 = 216 elementary events associated with the random experiment. 

We have, 

(A={(1,1,4), (1,2,4), (1,3,4), (1,4,4), (1,5,4), (1,6,4), (2,1,4) (2,2,4) , (2,3,4), (2,4,4), (2,5,4), (2,6,4), (3,1,4), (3,2,4), (3,3,4), (3,4,4), (3,5,4), (3,6,4), (4,1,4), (4,2,4), (4,3,4), (4,4,4), (4,5,4), (4,6,4), (5,1,4), (5,2,4), (5,3,4), (5,4,4), (5,5,4), (5,6,4), (6,1,4), (6,2,4), (6,3,4), (6,4,4), (6,5,4), (6,6,4)})

B={(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6)}