$A$ coin is tossed twice. If events $A$ and $B$ are defined as: $A = \text{head on first toss}$,$B = \text{head on second toss}$. Then the probability of $A \cup B = $

The probabilities of three mutually exclusive events are $\frac{2}{3}$,$\frac{1}{4}$,and $\frac{1}{6}$. The statement is:

If a card is drawn at random from a pack of $52$ cards,the probability that the card is a king or a diamond is $..........$.

From the employees of a company,$5$ persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows :

$S.No.$	Name	Sex	Age in years
$1.$	Harish	$M$	$30$
$2.$	Rohan	$M$	$33$
$3.$	Sheetal	$F$	$46$
$4.$	Alis	$F$	$28$
$5.$	Salim	$M$	$41$

$A$ person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over $35$ years?

If the odds against an event be $2 : 3$,then the probability of its occurrence is

If $A$ and $B$ are events such that $P(A \cup B) = \frac{5}{6}$, $P(\bar{A}) = \frac{1}{4}$, and $P(B) = \frac{1}{3}$, then $A$ and $B$ are