A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
A die thrown twice will have a total outcome of 62=36.
Let P(A) be the probability of getting the number 5 at least once.
Let P(B) be the probability of getting sum = 8.
The sample space of B = {(2,6),(3,5),(4,4),(5,3),(6,2)}
Let 
be the probability of getting the number 5 at least once and the sum equal to 8
The sample space of 
Tip – By conditional probability, 
where 
is the probability of occurrence of the event A given that B has already occurred.
The probability that the number 5 have appeared at least once given that the sum = 8:
1