Take two long dice (rectangular parallelepipeds), each having four rectangular faces labelled as 2, 3, 5, and 7. If thro...

Question

Take two long dice (rectangular parallelepipeds), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has an equal probability of landing on any of the four rectangular faces. The label on the top face of the die is the score of the throw. If thrown together, the probability that the sum of the two long dice scores is greater than 11 is:

A. 1/8   B. 1/16   C. 1/16   D. 3/16

Accepted Answer

P(sum > 11) = 3/16 Each long die has four faces labelled 2, 3, 5, 7 with equal probability 1/4. We throw two such dice and look at the sum of the top faces. We need P(sum > 11), which means P(sum >= 12). We list all pairs (die1, die2) that give a sum strictly greater than 11.