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:

$A$ die is thrown three times. Events $A$ and $B$ are defined as below:
$A$: $4$ on the third throw
$B$: $6$ on the first and $5$ on the second throw
Find the probability of $A$ given that $B$ has already occurred.

If $A$ and $B$ are two events such that $P(A \cup B) = P(A \cap B)$,then the true relation is

If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$,then which of the following is true?

$A$ family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

Let $E^{C}$ denote the complement of an event $E$. Let $E_{1}, E_{2}$ and $E_{3}$ be any pairwise independent events with $P(E_{1}) > 0$ and $P(E_{1} \cap E_{2} \cap E_{3}) = 0$. Then $P(E_{2}^{C} \cap E_{3}^{C} / E_{1})$ is equal to