# A standard pair of six sided dice is rolled. What is the probability of rolling a sum less than or equal to 10?

Feb 8, 2017

the probability is $\frac{1}{12}$

#### Explanation:

You will get 36 possible cases with two sided dices :

(1,1), (1,2),(1,3),...,(64),(6,5),(6,6)

but only these ones will give you a sum less than equal to 10:

(6,4),(4,6),(5,5)

Then the probability is:

$p = \frac{3}{36} = \frac{1}{12}$

Feb 9, 2017

$P \left(\text{sum} \le 10\right) = \frac{11}{12}$

#### Explanation:

There are 36 possible combinations from the two dice which are listed in this table:

The combination where the sum is less than or equal to 10 are coloured, and so

$P \left(\text{sum} \le 10\right) = \frac{36 - 3}{36} = \frac{33}{36} = \frac{11}{12}$