If two dice are rolled,then the probability of getting a multiple of $3$ as the sum of the numbers appeared on the top faces of the dice,given that their sum is an odd number,is

An unbiased die is thrown twice. Let the event $A$ be 'odd number on the first throw' and $B$ the event 'odd number on the second throw'. Check the independence of the events $A$ and $B$.

Two cards are drawn randomly from a pack of $52$ playing cards one after the other with replacement. If $A$ is the event of drawing a face card in the first draw and $B$ is the event of drawing a club card in the second draw,then $P(\overline{B}|A) = $

$A$ and $B$ are independent events of a random experiment if and only if

Suppose $A$ and $B$ are events of a random experiment such that $P(A)=\frac{1}{3}$,$P(A \cap B)=\frac{1}{5}$ and $P(A \cup B)=\frac{3}{5}$. Match the items of List-$I$ with the items of List-$II$.

List-$I$	List-$II$
$A$. $P(\frac{A}{B})$	$(i)$. $\frac{2}{15}$
$B$. $P(\bar{B})$	$(ii)$. $\frac{4}{15}$
$C$. $P(A \cap \bar{B})$	$(iii)$. $\frac{8}{15}$
$D$. $P(B \cap \bar{A})$	$(iv)$. $\frac{2}{3}$
	$(v)$. $\frac{3}{7}$

When $2$ dice are thrown,it is observed that the sum of the numbers appearing on the top faces of both dice is a prime number. What is the probability that at least one of the numbers in the pair is a multiple of $3$?