Problem Solving

Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.

M7MBA wrote:Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.

You found the probability that Peter would roll two of one particular number. If, for example, we wanted the probability that Peter rolled two 1's, you'd have been right. But he could have rolled two 2's or two 3's, etc.

Put another way, the total number of possible outcomes is 6*6 = 36.
The total number of ways to roll two of the same number would be 6. (two 1's, two 2's, two 3's, two 4's, two 5's, or two 6's.)
Probability of rolling two of the same number = 6/36 = 1/6. The answer is C

Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.

Hi M7MBA,
Let's take a look at your question.

Peter rolls two dice at a time, so let's first find the total number of outcomes.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

All possible outcomes when two dice are rolled at the same time = 36
We are asked to find the probability that he will roll a double.

The outcomes for rolling a double will be:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Total outcomes for rolling a double = 6

Probability of rolling a double = (Total outcomes for rolling a double) / (All possible outcomes when two dice are rolled)
Probability of rolling a double = 6/36 = 1/6

Therefore, Option C is correct.

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