Question

You roll two dice. What is the probability that the sum of the dice is prime and both dice show the number 6?

Answer 1

 The probability of both dice showing 6: 

The total possible outcomes of rolling 2 dice is 36. (1+1,1+2,..., 6+5, 6+6). Only one of these 36 rolls give two 6s. Hence, The probability of both dice showing 6 is 1/36 (1 in 36). 


We have 1 + 2 + 4+ 6 +2 ways to get prime rolls, which is a total of 15 ways. 
Hence the probability of getting a prime is 15/36.