Two dice and two coins are tossed. The probability that both the coins show head and the sum of the numbers found on the two dice is a prime number is?

The probability that head is show in one coin is 1/2.
The probability that the sum of the number on the dice is a prime = the probability that the following pair of number on the dice is a getting on the dice, namely (1, 1), (1, 2), (2, 1), (1, 4 ), (4, 1), (2, 3), (3, 2), (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3), (6, 5), (5, 6) = 15/36.
∴ The required probability = 1/2 x 1/2 x 15/36 = 5/48.