Question

When two dice are thrown, the sum on the two dice happened to be $7$. Find the probability that none of the dice shows a number $2$.

Answer 1

Given that the sum on two dice is $7$.

The possibilities of getting $7$ as sum are

$1,6$

$2,5$

$3,4$

$4,3$

$5,2$

$6,1$

Total number of possibilities is $6$ and among them the number of possibilities which shows $2$ is $2$.

Therefore the probability that none of the dice shows a number $2$ is $\frac{6-2}{6}=\frac{2}{3}$.