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.
