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?
We know, when a pair of dice is thrown, total possible outcomes are = 36
A=No of outcomes for getting sum of 8 are
{(2,6),(3,5),(4,4),(5,3),(6,2)} = 5
Therefore, P(A) =
B= No of outcomes for at least 5 has appeared once =
= {(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,5)} =11
Hence P(B) =
(A B) = outcomes of getting sum as 8 with at least one die showing 5
= {(3,5),(5,3)= 2
Hence P(A B)
Therefore, =
(answer)