NCERT Solutions for Class 9 Maths Chapter 15 Probability [Old Book]

NCERT
SOLUTIONS
CLASS - 9th

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Book - Mathematics Ncert Solutions | Chapter-15 Maths

Class : 9th
Subject : Maths
Chapter : 15
Chapter Name : Probability

Exercise 15.1

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 boundari = 6
Total number of balls played = 30
Number of times that the batwoman does not hit a boundary = 30 -6 = 24
Number of times when she does not hit boundary
p(she does not hit the boundary)= Total number of balls played

24 4
= =
30 5

Q2 1500 families with 2 children were selected randomly, and the following data were
recorded:

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

Number of families having 2 girls
p1(she does not hit the boundary)= Total number of balls played

475 19
= =
1500 60

(ii) Number of families having 1 girl =814

Number of families having 1 girl
p2(she does not hit the boundary)= Total number of balls played

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Book - Mathematics Ncert Solutions | Chapter-15 Maths

814 407
= =
1500 750

(iii) Number of families having no girl = 211

p3(she does not hit the boundary)=
Number of families having no girl

Total number of balls played

211
=
1500

Sum of all these probabilities = = 19

60
+
407

750
+
211

1500
475+814+211
=
1500
1500
= = 1
1500

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
Number of students born in August
P (Students born in the month of August) =
Total number of students
6 3
= =
40 20

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

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

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Book - Mathematics Ncert Solutions | Chapter-15 Maths

Number of times 2 heads come up
P(2 heads will come up ) =
Total number of times the coins were tossed
72 9
= =
200 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:

Suppose a family is chosen, nd 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, p=P = 579

2400

(ii) Number Of families earning Rs 16000 or more per month and owning exactly 1
vehicle = 579
Hence, required probability, p= 10

2400
=
240
1

(iii) Number of families earning less than Rs 7000 per month and dcmas not own any
vehicle = 10

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Book - Mathematics Ncert Solutions | Chapter-15 Maths

Hence, required probability, p= 10

2400
=
1

240

(iv) Number of families earning Rs 13000 - 16000 per month and owning more than
2 vehicles = 25
Hence, required probability, p= 25
=
2400
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, p= 2062
=
2400
1031

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. Total number Of students born in the year = 3 + 4 + 2 + 2 + 5 + 1 + 2 + 6 + 3 + 4 + 4 + 4 =
40
Number of students born in August
:. Probability that a student of the class was born in August = 6
=
40
3
.
20

Page : 284 , Block Name : Exercise 15.1

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.

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(student liking statistics)=
135 27
=
200 40

Page : 284 , Block Name : Exercise 15.1

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 1 2 km from her place of work?

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Book - Mathematics Ncert Solutions | Chapter-15 Maths

Answer. (i) Total number of engineers = 40
Number of engineers living less than 7 km from their place of work 9
Hence, required probability that an engineer lives less than 7 km from her place Of
P=
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 = 31

40

Hence, required probability that an engineer lives within km from her place of work, P = 0
1

2

Page : 284 , Block Name : Exercise 15.1

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. DIY

Page : 285 , Block Name : Exercise 15.1

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. DIY

Page : 285 , Block Name : Exercise 15.1

Q11 Eleven bags of wheat our, each marked 5 kg, actually contained the following weights of
our (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 our.

Answer. Number of total bags 11
Number of bags containing more than 5 kg of our = 7
Hence ,required probability P = 7

11

Page : 285 , Block Name : Exercise 15.1

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.

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Book - Mathematics Ncert Solutions | Chapter-15 Maths

Using this table, nd the probability of the concentration of sulphur dioxide in the interval
0.12 - 0.16 on any of these days.

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 P = 2
=
30
1

15

Page : 285 , Block Name : Exercise 15.1

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.

Answer. Number of students having blood group AB=3
Total number of students = 30
Hence,required probability P =
3 1
=
30 10

Page : 285 , Block Name : Exercise 15.1

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