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 $3$.

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?

In a cricket match,a batswoman hits a boundary $6$ times out of $30$ balls she plays. Find the probability that she did not hit a boundary.

Two coins are tossed simultaneously $500$ times,and we get:
Two heads : $105$ times
One head : $275$ times
No head : $120$ times
Find the probability of occurrence of each of these events.

$A$ teacher wanted to analyze the performance of two sections of students in a mathematics test of $100$ marks. Looking at their performances,she found that a few students got under $20$ marks and a few got $70$ marks or above. So she decided to group them into intervals of varying sizes as follows: $0-20, 20-30, ..., 60-70, 70-100$. Then she formed the following table:

Marks	Number of students
$0-20$	$7$
$20-30$	$10$
$30-40$	$10$
$40-50$	$20$
$50-60$	$20$
$60-70$	$15$
$70$ and above	$8$
Total	$90$

$(i)$ Find the probability that a student obtained less than $20\%$ in the mathematics test.
$(ii)$ Find the probability that a student obtained marks $60$ or above.

$A$ tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table shows the results of $1000$ cases.

Distance (in $km$)	less than $4000$	$4000$ to $9000$	$9001$ to $14000$	more than $14000$
Frequency	$20$	$210$	$325$	$445$

If you buy a tyre of this company,what is the probability that:
$(i)$ it will need to be replaced before it has covered $4000 \, km$?
$(ii)$ it will last more than $9000 \, km$?
$(iii)$ it will need to be replaced after it has covered somewhere between $4000 \, km$ and $14000 \, km$?