If $A$ and $B$ are arbitrary events, then
$P(A \cap B) \ge P(A) + P(B)$
$P(A \cup B) \le P(A) + P(B)$
$P(A \cap B) = P(A) + P(B)$
None of these
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'
A card is drawn from a pack of cards. Find the probability that the card will be a queen or a heart
Prove that if $E$ and $F$ are independent events, then so are the events $\mathrm{E}$ and $\mathrm{F}^{\prime}$.
$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. Then the probability of the two events are respectively
Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$, the probability that it is found to be red, is