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?

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 $1$.

$1500$ families with $2$ children were selected randomly,and the following data were recorded:

Number of girls in a family	$2$	$1$	$0$
Number of families	$475$	$814$	$211$

Compute the probability of a family,chosen at random,having:
$(i)$ $2$ girls $(ii)$ $1$ girl $(iii)$ No girl
Also,check whether the sum of these probabilities is $1$.

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.

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?

Ask all the students in your class to write a $3-$digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by $3$? Remember that a number is divisible by $3$,if the sum of its digits is divisible by $3$.