$A$ die has two faces each with number $1$,three faces each with number $2$,and one face with number $3$. If the die is rolled once,determine $P(2)$.

Let $S$ be a set of $5$ elements and $P(S)$ denote the power set of $S$. Let $E$ be an event of choosing an ordered pair $(A, B)$ from the set $P(S) \times P(S)$ such that $A \cap B = \varnothing$. If the probability of the event $E$ is $\frac{3^p}{2^q}$,where $p, q \in N$,then $p+q$ is equal to

Two dice are tossed once. The probability of getting an even number on the first die or a total of $8$ is

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $A$ and $B$.

If $A$ and $B$ are events such that $P(A \cup B) = 3/4,$ $P(A \cap B) = 1/4,$ and $P(\bar{A}) = 2/3,$ then $P(\bar{A} \cap B)$ is

Let $A$ and $B$ be two independent events of a random experiment. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$,then the probability of occurrence of $A$ is