The probability distribution of random variable $X$ with two missing probabilities $p_1$ and $p_2$ is given below

$X$	$P\left(X\right)$
$1$	$k$
$2$	$\begin{array}{l}{p}_1\end{array}$
$3$	$4\mathrm{k}$
$4$	$p_2$
$5$	$2\mathrm{k}$

It is further given that $P(X\le 2)=0.25$ and $P(X\ge 4)=0.35$

Consider the following statements

$\mathrm{I}.$ $p_1=p_2$

$\mathrm{II}.$ $p_1+p_2=P(X=3)$

Which of the statements is$/$are correct $?$

$A$ and $B$ are two events with positive probability, $P(A/B)$ is the conditional probability of $A$ given $B,$ and $\overline{A}$ is the complement of $A.$ 

Consider the following statements

$\mathrm{I}.$ $P(A/B)=P\left(A\right)\Rightarrow P(B/A)=P\left(B\right)$

$\mathrm{II}.$ $P(\overline{B}/A)=P\left(\overline{B}\right)\Rightarrow P(B/A)=P\left(B\right)$

$\mathrm{III}.$ $P(A\cap B)=P\left(A\right)·P\left(B\right)\Rightarrow P(\overline{A}\cap \overline{B})=P\left(\overline{A}\right)·P\left(\overline{B}\right)$

Which of the above statement(s) is / are correct?

Let $U=\{1, 2, 3, \dots , 20\}.$ Let $A, B$ and $C$ be the subsets of $U.$ Let $A$ be the set of all numbers, which are perfect squares, $B$ be the set of all numbers, which are multiples of $5$ and $C$ be the set of all numbers, which are divisible by $2$ and $3 ?$

Consider the following statements

$\mathrm{I}.$ $A, B$ and $C$ are mutually exclusive.

$\mathrm{II}.$ $A, B$ and $C$ are mutually exhaustive.

$\mathrm{III}.$ The number of elements in the complement set $A\cup B$ is $12.$

Which of the above statement(s) is$/$are correct?