A die is thrown three times,

E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

Determine P(E|F)

The sample space has 216 outcomes, where each element of the sample space has 3 entries and is of the form (x, y, z) where 1 ≤ x, y, z ≤ 6.

Here, E: 4 appears on the third toss

Now, F: 6 and 5 appears respectively on first two tosses

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

⇒ E ∩ F = {(6, 5, 4)}

So,

Now, we know that

By definition of conditional probability,