Problem Solving

Two dice are rolled. What is the probability the sum will be greater than 10?

A. 1/9.
B. 1/12.
C. 5/36.
D. 1/6.
E. 1/5.

The OA is B.

I need help with this PS question. Can any expert explain it for me please? Thanks.

Two dice are rolled. What is the probability the sum will be greater than 10?

A. 1/9.
B. 1/12.
C. 5/36.
D. 1/6.
E. 1/5.

The OA is B.

I need help with this PS question. Can any expert explain it for me please? Thanks.

Hi LUANDATO,
Let's take a look at your question.

When two dice are rolled, all possible outcomes will be:
$$\left(1,\ 1\right),\ \left(1,\ 2\right),\ \left(1,\ 3\right),\ \left(1,\ 4\right),\ \left(1,\ 5\right),\ \left(1,\ 6\right)$$
$$\left(2,\ 1\right),\ \left(2,\ 2\right),\ \left(2,\ 3\right),\ \left(2,\ 4\right),\ \left(2,\ 5\right),\ \left(2,\ 6\right)$$
$$\left(3,\ 1\right),\ \left(3,\ 2\right),\ \left(3,\ 3\right),\ \left(3,\ 4\right),\ \left(3,\ 5\right),\ \left(3,\ 6\right)$$
$$\left(4,\ 1\right),\ \left(4,\ 2\right),\ \left(4,\ 3\right),\ \left(4,\ 4\right),\ \left(4,\ 5\right),\ \left(4,\ 6\right)$$
$$\left(5,\ 1\right),\ \left(5,\ 2\right),\ \left(5,\ 3\right),\ \left(5,\ 4\right),\ \left(5,\ 5\right),\ \left(5,\ 6\right)$$
$$\left(6,\ 1\right),\ \left(6,\ 2\right),\ \left(6,\ 3\right),\ \left(6,\ 4\right),\ \left(6,\ 5\right),\ \left(6,\ 6\right)$$

Total possible outcomes = 36
Let's now find the outcomes where the sum of the numbers rolled on both the dice is more than 10 and that are:
$$\left(5,\ 6\right),\ \left(6,\ 5\right),\ \left(6,\ 6\right)$$

It means:
Total favorable outcomes = 3

Probability the sum will be greater than 10 = 3/36 = 1/12
Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.