Consider the frequency distribution table which gives the weights of $38$ students of a class.

Weights (in $kg$)	Number of students
$31-35$	$9$
$36-40$	$5$
$41-45$	$14$
$46-50$	$3$
$51-55$	$1$
$56-60$	$2$
$61-65$	$2$
$66-70$	$1$
$71-75$	$1$
Total	$38$

$(i)$ Find the probability that the weight of a student in the class lies in the interval $46-50 \, kg$.
$(ii)$ Give two events in this context,one having probability $0$ and the other having probability $1$.

An insurance company selected $2000$ drivers at random in a particular city to find a relationship between age and accidents. The data obtained are given in the following table:

Age of drivers (in years)	$0$ accidents	$1$ accident	$2$ accidents	$3$ accidents	Over $3$ accidents
$18-29$	$440$	$160$	$110$	$61$	$35$
$30-50$	$505$	$125$	$60$	$22$	$18$
Above $50$	$360$	$45$	$35$	$15$	$9$

Find the probabilities of the following events for a driver chosen at random from the city:
$(i)$ Being $18-29$ years of age and having exactly $3$ accidents in one year.
$(ii)$ Being $30-50$ years of age and having one or more accidents in a year.
$(iii)$ Having no accidents in one year.

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 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.

Eleven bags of wheat flour,each marked $5 \,kg$,actually contained the following weights of flour (in $kg$):
$4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00$
Find the probability that any of these bags chosen at random contains more than $5 \,kg$ of flour.

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.