If $A$ and $B$ are two independent events,then $P\left( \frac{A}{B} \right) = $

If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

If $A$ and $B$ are two events such that $P(A | B) = 0.6$,$P(B | A) = 0.3$,and $P(A) = 0.1$,then $P(\bar{A} \cap \bar{B})$ equals:

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

If $A$ and $B$ are any two events such that $P(A) = \frac{2}{5}$ and $P(A \cap B) = \frac{3}{20}$,then the conditional probability $P(A | A' \cup B')$,where $A'$ denotes the complement of $A$,is equal to:

In a group of $14$ males and $6$ females,$8$ males and $3$ females are aged above $40 \text{ yr}$. The probability that a person selected at random from the group is aged above $40 \text{ yr}$,given that the selected person is a female,is: