# 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 (6^{2} = 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