If $A$ and $B$ are mutually exclusive events,then the value of $P(A \cup B)$ is

For two given events $A$ and $B$,$P(A \cap B)$ is:

The probability of an event happening is the square of the probability of a second event,but the odds against the first are the cube of the odds against the second. The probabilities of the events are:

If $A$ and $B$ are two events in a random experiment such that $P(A) + P(B) = 2 P(A \cap B)$, then:

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?

The probabilities that $A$ and $B$ speak the truth are $\frac{4}{5}$ and $\frac{3}{4}$ respectively. The probability that they contradict each other when asked to speak on a fact is