NCERT Solutions for Class 9 Maths Chapter 15 Probability

Q1 ) 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.

Answer :

Number of times the batswoman hits a boundary = 6

Total number of balls played = 30

Thus, Number of times that the batwoman does not hit a boundary
= 30 - 6
= 24

So, we get that,

$P=\frac{Numberoftimeswhenshedoesnothitboundary}{Totalnumberofballsplayed}$
$P=\frac{24}{30}=\frac{4}{5}$

Therefore, the probability that she did not hit a boundary is $\frac{4}{5}$.

Q2 ) 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 weather the sum of these probabilities is 1.

Answer :

Total number of family = 475 + 814 + 211 = 1500

i) number of families of 2 girls = 475

So, we get that,

P1 =$\frac{Numberoffamilieshaving2girls}{Totalnumberoffamily}$
p =$\frac{475}{1500}=\frac{19}{60}$.

Therefore, the probability of a family, chosen at random, is having 2 girls

ii) Number of families having 1 girl = 814

So, we get that,

P2 = $\frac{Numberoffamilieshaving1girls}{Totalnumberoffamily}$
p = $\frac{814}{1500}=\frac{407}{750}$..

Therefore, the probability of a family, chosen at random, is having 2 girls

iii) Number of families having no girl = 211
So, we get that,

$P3=\frac{Numberoffamilieshaving0girls}{Totalnumberoffamily}$
$p=\frac{211}{1500}$.

Therefore, the probability of a family, chosen at random, is having 2 girls

Now, Sum of all these probabilities
= P1 + P2 + P3
= $\frac{19}{60}+\frac{407}{750}+\frac{211}{1500}$
$=\frac{475+814+211}{1500}$
$=\frac{1500}{1500}=1$

Hence, we can say that,
The sum of these probabilities is 1.

Q3 ) Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

Answer :

Number of students born in the month of August = 6
Total number of students = 40

$P=\frac{NumberofstudentsborninAugust}{Totalnumberofstudents}$
$P=\frac{6}{40}=\frac{3}{20}$.

Therefore, the probability that a student of the class was born in August is $\frac{3}{20}$.

Q4 ) Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	3 heads	2 heads	1 heads	0 head
Frequency	23	72	77	28

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

Answer :

Number of times 2 heads come up = 72
Total number Of times the coins were tossed = 200

$P=\frac{Numberoftimes2headscomeup}{Totalnumberoftimesthecoinsweretossed}$
$P=\frac{72}{200}=\frac{9}{25}$

Therefore, the probability of 2 heads coming up is $\frac{9}{25}$.

Q5 ) 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
1300 - 16000	2	469	59	25
1600 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 I 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.

Answer :

Number of total families surveyed
= 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400

i) Number of families earning Rs. 10000 - 13000 per month and owning exactly 2 vehicles = 29
Hence, required probability is $P=\frac{579}{2400}$

ii) Number Of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
Hence, required probability is $P=\frac{10}{2400}=\frac{1}{240}$

iii) Number of families earning less than Rs. 7000 per month and dcmas not own any vehicle = 10
Hence, required probability is $P=\frac{10}{2400}=\frac{1}{240}$

iv) Number of families earning Rs. 13000 - 16000 per month and owning more than 2 vehicles = 25
Hence, required probability is $P=\frac{25}{2400}=\frac{1}{96}$

v)Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 535 + 2 + 469 + 1 + 579 = 2062
Hence, required probability is $P=\frac{2026}{2400}=\frac{1013}{1200}$

Q6 ) Refer to Table 14.7, Chapter 14.
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.

Answer :

i) Number of students obtained less than 20% in the mathematics test = 7

Total number of students = 90
Thus, $P=\frac{7}{90}$

Therefore, the probability that a student obtained less than 20% in the mathematics test is $\frac{7}{90}$.

ii) Number of students obtained 60 or above marks = 23
Total number of students = 90
Thus, $P=\frac{23}{90}$

Therefore, the probability that a student obtained marks 60 or above is $\frac{23}{90}$.

Q7 ) To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.

Opinion	Number of students
like	135
Dislike	65

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

Answer :

Total number of students
= 135 + 65 = 200

i) Number of students liking statistics = 135
$P=\frac{135}{200}=\frac{27}{40}$

Therefore, the probability of student liking statistics is $\frac{27}{40}$

ii) Thus, Probability of students that students dont like statistics is
$=P=1?\frac{135}{200}=\frac{65}{200}=\frac{13}{40}$

Therefore, the probability of student not liking statistics is $\frac{13}{40}$.

Q8 ) Refer to Q.2, Exercise 14.2. 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?

Answer :

i) Total number of engineers = 40
Also, Number of engineers living in less than 7 km from their place of work = 9
Hence, required probability that an engineer lives less than 7 km from her place =
$P=\frac{9}{40}$

ii) Number of engineers living more than or equal to 7 km from their place of work = 40 - 9 = 31
Hence, required probability that an engineer lives more than or equal to 7 km from her place of work =
$P=\frac{31}{40}$

iii)Hence, required probability that an engineer lives within $\frac{1}{2}$ km from her place of work is P = 0.

Q9 ) 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.

Answer :

Perform the activity by yourself and note down your observations.

Q10 ) Activity : 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.

Answer :

Perform the activity by yourself and note down your observations.

Q11 ) 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.

Answer :

Number of total bags = 11
Number of bags containing more than 5 kg of flour = 7
Hence, required probability = $P=\frac{7}{11}$

Therefore, the probability that any of these bags chosen at random contains more than 5 kg of flour is $\frac{7}{11}$.

Q12 ) In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.
Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on any of these days.

Concentration of $S\left(O_2\right)$ (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

Answer :

Number days for which the concentration Of sulphur dioxide was in the interval of 0.12 - 0.16 = 2

Total number Of days = 30

Hence, required probability is $P=\frac{2}{30}=\frac{1}{15}$.

Therefore, the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on any of these days is $\frac{1}{15}$.

Q13 ) In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

Blood Group	Number of students
O	12
A	9
B	6
AB	3

Answer :

Number of students having blood group AB = 3

Total number of students = 30
Hence, required probability is $P=\frac{3}{30}=\frac{1}{10}$.

Therefore, the probability that a student of this class, selected at random, has blood group AB is $\frac{1}{10}$.