$A$ family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

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

From a group of $8$ boys and $3$ girls,a committee of $5$ members is to be formed. Find the probability that $2$ particular girls are included in the committee.

If $4\,P(A) = 6\,P(B) = 10\,P(A \cap B) = 1$,then $P\left( \frac{B}{A} \right) = \dots$

$A$ box contains $3$ white and $2$ red balls. $A$ ball is drawn and another ball is drawn without replacing the first ball. What is the probability that the second ball is red?

Compute $P(A | B),$ if $P(B)=0.5$ and $P(A \cap B)=0.32$.