$A$ black and a red dice are rolled. Find the conditional probability of obtaining the sum $8$,given that the red die resulted in a number less than $4$.

$A$ die is thrown twice and the sum of the numbers appearing is observed to be $6$. What is the conditional probability that the number $4$ has appeared at least once?

Two numbers are selected at random from the set $\{1, 2, 3, \ldots, 13\}$. If the sum of the selected numbers is even, what is the probability that both the numbers are odd?

Two dice are rolled. If $A$ denotes the event that the same number shows on each die and $B$ denotes the event that the sum of the numbers on both dice is greater than $7$,then $P(A \mid B)$ and $P(B \mid A)$ respectively are

$A$ couple has two children. If at least one of them is a boy,then the probability that the other is also a boy is:

In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. If she reads English newspaper,find the probability that she reads Hindi newspaper.