The probability that a leap year selected at random contains either $53$ Sundays or $53$ Mondays is:

If $A, B, C$ are three events associated with a random experiment,prove that $P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$.

Fill in the blank in the following table:

$P(A)$	$P(B)$	$P(A \cap B)$	$P(A \cup B)$
$0.35$	$..........$	$0.25$	$0.6$

If $A$ and $B$ are mutually exclusive events,then the value of $P(A \cup B)$ 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 $A$ and $B$ are two events of a random experiment such that $P(A \cup B) = 0.65$ and $P(A \cap B) = 0.15$,then $P(\overline{A}) + P(\overline{B}) = $