What is the probability of getting a doublet when two dice are thrown?

Two fair dice are thrown simultaneously. The probability of getting the same number on both dice is $......$.

$A$ bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected at random, the probability that it is a black or a red ball, is

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$, then $P(\bar{A})+P(\bar{B})$ is equal to:

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