If $A$ and $B$ are two events of a random experiment such that $P(A)=0.6$,$P(B)=0.3$,and $P(A \mid B)=0.5$,then $P(\bar{B} \mid \bar{A})=$

If $\overline{E}$ and $\overline{F}$ are the complementary events of events $E$ and $F$ respectively and if $0 < P(F) < 1$,then

When a die is thrown twice,what is the probability that the sum of the numbers is $6$,given that at least one of the numbers is $4$?

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.

Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to