M7MBA wrote:Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?

A) 5/11
B) 5/12
C) 5/21
D) 2/9
E) 5/36

The OA is the option B.

I thought the correct answer was A=5/11. Can anyone explain to me why is B? Thanks in advanced.

Hello M7MBA.

Let's see the question. We need to find all the possible cases: for the first die we have 6 different options and for the second die we also have 6 different options. Therefore, we have 6*6=36 different options.

Now, the sum of the two dies can be: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. From these numbers, we are interested in the prime numbers, that is to say: 2, 3, 5, 7, 11.

The number of ways to get each prime number are:

Nº ---------- Die 1----Die 2
2 -------------- 1 ------- 1

3 -------------- 1 ------- 2
3 -------------- 2 ------- 1

5 -------------- 1 ------- 4
5 -------------- 2 ------- 3
5 -------------- 3 ------- 2
5 -------------- 4 ------- 1

7 -------------- 1 ------- 6
7 -------------- 2 ------- 5
7 -------------- 3 ------- 4
7 -------------- 4 ------- 3
7 -------------- 5 ------- 2
7 -------------- 6 ------- 1

11 ------------ 5 ------- 6
11 ------------ 6 ------- 5

We have a total of 15 favorable cases.

Therefore, the probability that the sum of the exposed faces on the die is a prime number is equal to $$P=\frac{15}{36}=\frac{5}{12}.$$ This implies that the correct answer is the option B.

I hope it can be clear.