# If you roll two fair six-sided dice, what is the probability that the sum is 5 or lower?

**Solution:**

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by x

Let ‘x’ be the number on the first dice.

‘Y’ be the number on second dice.

We have to find the probability that the sum is 5 or lower i.e. (x + y) <= 5.

Total number of possible results from two six-sided dice is 6 × 6 = 36.

The possible results that the sum is lower than 4 is (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2) and (4,1).

Number of possible results for the sum is 5 or lower is 10.

The probability that the sum is 5 or lower = 10/36

=5/18

Therefore, the probability that the sum is 5 or lower is 5/18.

## If you roll two fair six-sided dice, what is the probability that the sum is 5 or lower?

**Summary:**

If you roll two fair six-sided dice, the probability that the sum is 5 or lower is 5/18.