A die is thrown three times, E: 4 appears on the third toss, and 5 appears respectively on first two tosses.

Solution:

In the sample space, there are 216 outcomes, with each element of the sample space having three entries and taking the form

where .

Considering the event, E: 4 appears on the third toss

   

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

   

So,

Now, we know that by definition of conditional probability,

Now by substituting the values we get