question

[sukh]

If two fair six-sided dice are thrown, what is the probability that
the sum of the numbers showing on the dice is a prime number?
(A) 5/11
(B) 5/12
(C) 1/2
(D) 7/12
(E) 7/9

[Geva@EconomistGMAT]

If two fair six-sided dice are thrown, what is the probability that
the sum of the numbers showing on the dice is a prime number?
(A) 5/11
(B) 5/12
(C) 1/2
(D) 7/12
(E) 7/9

The sum of 2 dice can reach up to 12.
Primes up to 12 are 2, 3, 5, 7, 11

So out of 6*6=36 possible combinations, the wanted ones are

2: 1+1

3: 1+2, 2+1

5: 1+4, 4+1, 2+3, 3+2

7: 1+6, 6+1, 2+5, 5+2, 3+4, 4+3

11: 5+6, 6+5

total of 15 wanted combinations, for a final probability of 15/36 = 5/12

[cans]

sum can be max 12. prime numbers = 2,3,5,7,11.
11 -> (5,6): 1*2 = 2
7: (1,6),(2,5),(3,4)= 6
5 (1,4)(2,3) - 4
3 (1,2) 2
2 (1,1) 1
ttoal = 15
prob = 15/36 = 5/12
IMO B