If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places)
getting a sum of 1?
getting a sum of 5?
getting a sum of 12?

Solution:

The total number of outcomes if we roll a pair of fair dice is 36 (6² = 36).

This can be verified by writing down all the outcomes.

The probability of getting a sum 1 on the roll of two fair dice

= No. of outcomes with sum = 1

Now there are no outcomes where the sum of the two dice is 1, it implies

P(sum of 1 on roll of two dice) = 0/36 = 0

The combinations of a pair of dice which produce the sum of 5 are as follows:

(1, 4), (4,1), (2, 3), (3. 2).

Therefore,

P(sum of 5 on roll of two dice) = 4/36 = 1/9 = 0.1111

The combinations of a pair of dice which produce the sum of 12 are as follows:

(6,6), (5,7), (7,5)

P(sum of 12 on roll of two dice) = 3/36 = 1/12 = 0.0833.

If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places)
getting a sum of 1?
getting a sum of 5?
getting a sum of 12?

Summary:

If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places). The probabilities are :

P(sum of 1 on roll of two dice) = 0/36 = 0, P(sum of 5 on roll of two dice) = 4/36 = 1/9 = 0.1111, P(sum of 12 on roll of two dice) = 3/36 = 1/12 = 0.0833