Three coins are tossed simultaneously $200$ times with the following frequencies of different outcomes:

Outcome	$3$ heads	$2$ heads	$1$ head	No head
Frequency	$23$	$72$	$77$	$28$

If the three coins are simultaneously tossed again,compute the probability of $2$ heads coming up.

The distance (in $km$) of $40$ engineers from their residence to their place of work were found as follows.

$5$	$3$	$10$	$20$	$25$	$11$	$13$	$7$	$12$	$31$
$19$	$10$	$12$	$17$	$18$	$11$	$32$	$17$	$16$	$2$
$7$	$9$	$7$	$8$	$3$	$5$	$12$	$15$	$18$	$3$
$12$	$14$	$2$	$9$	$6$	$15$	$15$	$7$	$6$	$12$

What is the empirical probability that an engineer lives:
$(i)$ less than $7 \, km$ from her place of work?
$(ii)$ more than or equal to $7 \, km$ from her place of work?
$(iii)$ within $\frac{1}{2} \, km$ from her place of work?

The following frequency distribution table shows the blood groups of $30$ students of a class. Use this table to determine the probability that a student of this class,selected at random,has blood group $AB$.

Blood group	Number of students
$A$	$9$
$B$	$6$
$AB$	$3$
$O$	$12$
Total	$30$

The following frequency distribution table shows the concentration of sulphur dioxide $(SO_2)$ in the air in parts per million $(ppm)$ of a certain city for $30$ days. Using this table,find the probability of the concentration of sulphur dioxide being in the interval $0.12 - 0.16$ on any of these days.

Concentration of $SO_2$ (in $ppm$)	Number of days (frequency)
$0.00-0.04$	$4$
$0.04-0.08$	$9$
$0.08-0.12$	$9$
$0.12-0.16$	$2$
$0.16-0.20$	$4$
$0.20-0.24$	$2$
Total	$30$

The record of a weather station shows that out of the past $250$ consecutive days,its weather forecasts were correct $175$ times.
$(i)$ What is the probability that on a given day it was correct?
$(ii)$ What is the probability that it was not correct on a given day?

An organisation selected $2400$ families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

Monthly income (in Rs.) / Vehicles per family	$0$	$1$	$2$	Above $2$
Less than $7000$	$10$	$160$	$25$	$0$
$7000 - 10000$	$0$	$305$	$27$	$2$
$10000 - 13000$	$1$	$535$	$29$	$1$
$13000 - 16000$	$2$	$469$	$59$	$25$
$16000$ or more	$1$	$579$	$82$	$88$

Suppose a family is chosen. Find the probability that the family chosen is:
$(i)$ Earning Rs. $10000 - 13000$ per month and owning exactly $2$ vehicles.
$(ii)$ Earning Rs. $16000$ or more per month and owning exactly $1$ vehicle.
$(iii)$ Earning less than Rs. $7000$ per month and does not own any vehicle.
$(iv)$ Earning Rs. $13000 - 16000$ per month and owning more than $2$ vehicles.
$(v)$ Owning not more than $1$ vehicle.