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,