If $A$ and $B$ are two events such that $P(A)=\frac{1}{2}$,$P(B)=\frac{1}{2}$ and $P(A \mid B)=\frac{1}{4}$,then $P(A^{\prime} \cap B^{\prime})$ is

From a lot containing $n$ good and $m$ bad articles, if $2$ articles are picked at random in succession without replacement, then the probability that the second article picked is bad is

Evaluate $P(A \cup B)$,if $2 P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$.

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 $4$?

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?

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