Three dice are rolled. Given that the sum of the numbers is 15, the probability that the first die shows a 6 is:

Three dice are rolled. Given that the sum of the numbers is 15, the probability that the first die shows a 6 is:

• A. 2/5
• B. 1/5
• C. 3/10
• D. 1/3

Answer: A) 2/5

Explanation: Combinations for sum 15: (3,6,6)x3, (4,5,6)x6, (5,5,5)x1 = 10 ways. Favourable cases where first die is 6: (6,3,6), (6,6,3), (6,4,5), (6,5,4) = 4 ways. Probability = 4/10 = 2/5.