Given that $A$ and $B$ are two events such that $P(B) = \frac{3}{5}$,$P\left(\frac{A}{B}\right) = \frac{1}{2}$,and $P(A \cup B) = \frac{4}{5}$,then $P(A)$ is equal to:

If $P(A) = \frac{7}{13}$,$P(B) = \frac{9}{13}$ and $P(A \cap B) = \frac{4}{13}$,evaluate $P(A | B)$.

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

Three coins are tossed. If one of them shows tail,then the probability that all three coins show tail,is

$A, B$ are the events in a random experiment. If $P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(A \cap B)=\frac{1}{4}$, then $P\left(\frac{A^{c}}{B^{c}}\right)+P\left(\frac{A}{B}\right)=$

Let $A$ and $B$ be two independent events such that $P(A) + P(B) = \frac{3}{4}$ and $P(\overline{A} | B) = \frac{2}{5}$. Then,$P(A \cap B)$ is -