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.

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	$30$

Note the frequency of two-wheelers, three-wheelers, and four-wheelers passing by your school gate during a specific time interval. Calculate the probability that any one vehicle chosen from the total vehicles observed is a two-wheeler.

Find the probability that a student of the class was born in August.

The percentage of marks obtained by a student in the monthly unit tests are given below:

Unit test	$I$	$II$	$III$	$IV$	$V$
Percentage of marks obtained	$69$	$71$	$73$	$68$	$74$

Based on this data,find the probability that the student gets more than $70\%$ marks in a unit test.