A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the probability that the number 4 has appeared at least once?

A = Sum of the numbers appearing on two dice is 6 = {(1,5), (5,1), (2,4), (4,2) (3,3)}

B = Number 4 has appeared at least once = {(1,4), (4,1), (2,4), (4,2) (3,4), (4,3) (4,4), (4,5), (5,4), (4,6), (6,4)}

Required Probability = P(B/A)

= n(A ∩ B) / n(A)

= 2 / 5