A pair of dice are thrown together. The probability that the sum of both the outcomes is less than 11 is ___

The probability of an event is the number of favourable outcomes divided by the total number of possible outcomes.

The sample space is as follows:

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

​(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

​(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

​(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

​(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

​(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Then apply the above formula to get the final answer. 

When two dice are thrown, there are 36 possible outcomes.

All of the outcomes are favourable except$(6,6),(6,5)$, and $(5,6)$ whose sum is equal to or more than 11 .

Therefore$36-3=33$ outcomes that are favorable.

Hence,

$\mathrm{P}(\mathrm{sum}<11)=\frac{33}{36}=\frac{11}{12}$