$A$ card is drawn from a pack of $52$ cards. Find the probability that the card will be a queen or a heart.

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 $E$ and $F$ are events such that $P(E) = \frac{1}{4}$,$P(F) = \frac{1}{2}$ and $P(E \cap F) = \frac{1}{8}$,find $P(E \cup F)$.

The two events $A$ and $B$ have probabilities $0.25$ and $0.50$ respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then the probability that neither $A$ nor $B$ occurs is

There are three events $A, B, C$,one of which must and only one can happen. The odds are $8:3$ against $A$,$5:2$ against $B$,and the odds against $C$ are $43:17k$. Then the value of $k$ is:

If the odds against $A$ solving a problem are $4:3$ and the odds in favor of $B$ solving the problem are $7:5$,what is the probability that only one of them solves the problem?