Question

A die is thrown twice and the sum of the numbers appearing is observed to be $7$. Find the conditional probability that the number $3$ has appeared at least once.

Answer 1

Total options for numbers on the die for the sum to be 7 are as below:

$1+6,6+1,2+5,5+2,3+4,4+3$

Thus, there are 6 ways possible for the sum to be 7.

Out of these six ways, there are 2 ways where 3 is one of the outcome and so the probability of occurrence of 3 becomes $\frac{3}{6}=\frac{1}{2}$