If $A$ and $B$ are two events such that $P\,(A \cup B) = P\,(A \cap B),$ then the true relation is
$P\,(A) + P\,(B) = 0$
$P\,(A) + P\,(B) = P\,(A)\,P\,\left( {\frac{B}{A}} \right)$
$P\,(A) + P\,(B) = 2\,P\,(A)\,P\,\left( {\frac{B}{A}} \right)$
None of these
If $A$ and $B$ are two events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{2}{3},$ then
A fair coin and an unbiased die are tossed. Let $A$ be the event ' head appears on the coin' and $B$ be the event ' $3$ on the die'. Check whether $A$ and $B$ are independent events or not.
Given $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$. Find $P(A $ or $B),$ if $A$ and $B$ are mutually exclusive events.
Let $A$ and $B$ are two events and $P(A') = 0.3$, $P(B) = 0.4,\,P(A \cap B') = 0.5$, then $P(A \cup B')$ is
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 ?
$\mathrm{E}:$ ' the card drawn is black '
$\mathrm{F}:$ ' the card drawn is a king '