Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability $0.7$ whereas George,independently,hits the target with probability $0.4$. Given that exactly one shot hit the target,what is the probability that it was George's shot?

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 black'
$F:$ 'the card drawn is a king'

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is $0.9$ and that of the second unit is $0.8$. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and the second unit is functioning is $p$,then $98p$ is equal to ..... .

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 -

If $P(A) = \frac{1}{2}$ and $P(B) = 0$,then $P(A | B)$ is

If $A$ and $B$ are two events such that $P(A) = \frac{1}{3}$,$P(B) = \frac{1}{4}$ and $P(A \cap B) = \frac{1}{5}$,then $P\left( \frac{\overline{B}}{\overline{A}} \right) = $