Question

In a simultaneous throw of a  pair of dice, find the probability of getting: 

a sum less than 6

Answer 1

$$\text{ When a pair of dice is thrown simultaneously, the sample space will be as follow }:$$
$$S=\{(1,1),(1,2),(1,3),(1,4),\cdots (6,5),(6,6)\}$$
$$\text{ Hence, the total number of outcomes is 36 }.$$ 

$$\text{ Let A be the event of getting pairs whose sum is less than 6 }.$$
$$\text{ The pairs whose sum is less than 6 are }(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2)\text{ and }(4,1).$$
$$\text{ Hence, the number of favourable outcomes is }10.$$
$$\therefore P\left(A\right)=\frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }}=\frac{10}{36}=\frac{5}{18}$$