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

No. of girls in a family	$2$	$1$	$0$
No. 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 $1$.

Q. Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Q. The distance (in km) of $40$ engineers from their residence to their place of work were found as follows:
$\begin{array}{cccccccccc}5& 3& 10& 20& 25& 11& 13& 7& 12& 31\\ 19& 10& 12& 17& 18& 11& 32& 17& 16& 2\\ 7& 9& 7& 8& 3& 5& 12& 15& 18& 3\\ 12& 14& 2& 9& 6& 15& 15& 7& 6& 12\end{array}$
What is the empirical probability that an engineer lives:
(i) less than $7km$ from her place of work?
(ii) more than or equal to $7km$ from her place of work?
(iii) within $\frac{1}{2}km$ from her place of work?

Q. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
$\begin{array}{cccccc}0.03& 0.08& 0.08& 0.09& 0.04& 0.17\\ 0.16& 0.05& 0.02& 0.06& 0.18& 0.20\\ 0.11& 0.08& 0.12& 0.13& 0.22& 0.07\\ 0.08& 0.01& 0.10& 0.06& 0.09& 0.18\\ 0.11& 0.07& 0.05& 0.07& 0.01& 0.04\end{array}$
Using this table, find the probability of the concentration of sulphur dioxide in the interval $0.12-0.16$ on any of these days.

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

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

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

Q. In a class of $40$ students, ask them to write a 3-digit number. Choose any student 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.

Q. A teacher wanted to analyze the performance of two sections of students in a mathematics test of 100 marks. Looking at their performance, 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.
(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.

Q. 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.

Q. Eleven bags of wheat flour, each marked $5kg$, actually contained the following weights of flour (in kg):
$4.975.055.085.035.005.065.084.985.045.075.00$
Find the probability that any of these bags chosen at random contains more than $5kg$ of flour.

Q. The blood groups of 30 students of Class VIII are recorded as follows:
$A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O,$
$A,AB,O,A,A,O,O,AB,B,A,O,B,A,B,O$.
Use this table to determine the probability that a student of this class, selected at random, has blood group $AB$.

Q. Find the probability that a student chosen at random
(i) likes statistics.
(ii) does not like statistics.

Q. 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.

Q. In a particular section of class IX, 40 students were asked about the month of their birth and following graph was prepared for data so obtained:
Find the probability that a student of the class was born in August.