Question

If two fair dice are rolled, what is the probability that a total of four shows?

A. 1/18

B. 1/9

C. 5/36

D. 1/12

Answer 1

2 fair dice are rolled.

We have to find the probability that a total of 4 shows.

Now, when two dice are rolled, the first dice can show any of the 6 outcomes (1,2,3,4,5,6); the second dice, independent of the first, can also show any of the 6 outcomes (1,2,3,4,5,6).

So, on rolling two fair dice, the total number of possible outcomes is 6*6, ie. 36.

ie. the number of all possible outcomes is 36.

Now, a total of 4 shows up when the outcomes are

(1,3), (2,2), (3,1).

So, there are 3 favourable outcomes.

Now, we know that the probability of an event is nothing but the ratio of the number of favourable outcomes for the event, to the number of all possible cases.

So, we can say

P(A total of 4 shows)

=3/36

=1/12

The answer is

If two fair dice are rolled, the probability that a total of four shows is option (D) 1/12.