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.
