A die is thrown twice and the sum of numbers appearing is observed to be 8 . What is the conditional probability that the number 5 has appeared atleast once?

Step-by-step solution

Let S be the sample space of throwing a die twice. The total number of outcomes is 6 6 = 36 . Let A be the event that the sum of the numbers appearing is 8. The possible outcomes for A are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) . Thus, n(A) = 5 . Let B be the event that the number 5 has appeared at least once. We are looking for the conditional probability P(B|A) = n(A B) n(A) . The intersection A B consists of outcomes in A where at least one die shows 5. These are (3, 5) and (5, 3) . Thus, n(A B) = 2 . Therefore,