Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6$,the probability of getting a sum as $3$ is:

Consider the following statements.
Statement $(I)$: If $E$ and $F$ are two independent events,then $E^{\prime}$ and $F^{\prime}$ are also independent.
Statement $(II)$: Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent.
Which of the following is correct?

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

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

If $E_1$ and $E_2$ are two events of the sample space such that $P(E_1) = \frac{1}{4}$, $P(E_1 | E_2) = \frac{1}{2}$ and $P(E_2 | E_1) = \frac{1}{3}$, then $P(E_1 | \bar{E}_2) = $

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B|A)$,if $A$ is a subset of $B$.