The probabilities of Virat becoming the Man of the Match in the $1^{st}$,$2^{nd}$,and $3^{rd}$ matches of India in the World Cup $2015$ are $\frac{3}{7}$,$\frac{2}{7}$,and $\frac{1}{7}$ respectively. If Virat got the Man of the Match in exactly one match,what is the probability that he got it in the $3^{rd}$ match?

Two dice are thrown simultaneously. If $A$ is the event of getting the sum of the numbers on two dice as greater than or equal to $8$ and $B$ is the event of getting a number less than or equal to $3$ on at least one of the dice. Then,$P(B / A) = $

Two dice $A$ and $B$ are rolled. If it is known that the number on $B$ is $5$,then the probability that the sum of the numbers on the two dice will be greater than $9$ is

Out of $50$ tickets numbered $00, 01, 02, \dots, 49$,one ticket is drawn at random. Let $A$ be the event that the sum of the digits on the ticket is $8$,and $B$ be the event that the product of the digits is $0$. Find the conditional probability $P(A|B)$.

An urn contains $5$ red and $5$ black balls. $A$ ball is drawn at random,its colour is noted and is returned to the urn. Moreover,$2$ additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

Consider three sets $E_1=\{1,2,3\}, F_1=\{1,3,4\}$ and $G_1=\{2,3,4,5\}$. Two elements are chosen at random,without replacement,from the set $E_1$,and let $S_1$ denote the set of these chosen elements.
Let $E_2=E_1-S_1$ and $F_2=F_1 \cup S_1$. Now two elements are chosen at random,without replacement,from the set $F_2$ and let $S_2$ denote the set of these chosen elements.
Let $G_2=G_1 \cup S_2$. Finally,two elements are chosen at random,without replacement,from the set $G_2$ and let $S_3$ denote the set of these chosen elements.
Let $E_3=E_2 \cup S_3$. Given that $E_1=E_3$,let $p$ be the conditional probability of the event $S_1=\{1,2\}$. Then the value of $p$ is