A card is drawn from a pack of cards. Find the probability that the card will be a queen or a heart

If $A$ and $B$ are two independent events such that $P(A) > 0.5,\,P(B) > 0.5,\,P(A \cap \bar B) = \frac{3}{{25}},\,P(\bar A \cap B) = \frac{8}{{25}}$ , then $P(A \cap B)$ is 

Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac {1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?

$E:$ ' the card drawn is a king and queen '

$F:$  ' the card drawn is a queen or jack '

If $P(B) = \frac{3}{4}$, $P(A \cap B \cap \bar C) = \frac{1}{3}{\rm{ }}$ and $P(\bar A \cap B \cap \bar C) = \frac{1}{3},$ then $P(B \cap C)$ is

One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?

$E:$ 'the card drawn is a spade'

$F:$ 'the card drawn is an ace'