Given $P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3$,then $P(A^{\prime} / B^{\prime})$ is equal to

In a random experiment,events $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A \mid B) = \frac{1}{2}$,and $P(B \mid A) = \frac{2}{3}$. Find $P(B)$.

One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?
$E:$ 'the card drawn is a spade'
$F:$ 'the card drawn is an ace'

Ten cards numbered $1$ to $10$ are placed in a box,mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3,$ what is the probability that it is an even number (in $/7$)?

If $A$ and $B$ are two events of a sample space $S$ such that $P(A)=0.2$,$P(B)=0.6$ and $P(A \mid B)=0.5$,then $P(A^{\prime} \mid B) = $

If $C$ and $D$ are two events such that $P(D) \neq 0$,then which of the following statements is correct?