Maths NCERT solutions class 9 Chapter 15 PROBABILITY

Table of Contents

15. PROBABILITY

15.1 Introduction
15.2 Probability – an Experimental Approach
15.3 Summary

Maths NCERT solutions class 9 Chapter 15 PROBABILITY

Important formula

Exercise 15.1

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Q.1. 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.

Total numbers of balls = 30
Numbers of boundary = 6
Numbers of time she didn’t hit boundary = 30 – 6 = 24
Probability she did not hit a boundary = 24/30 = 4/5

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

Number of girls in a family210
Number of families475814211

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.

Total numbers of families = 1500
(i) Numbers of families having 2 girls = 475
Probability = Numbers of families having 2 girls/Total numbers of families
= 475/1500 = 19/60
(ii) Numbers of families having 1 girls = 814
Probability = Numbers of families having 1 girls/Total numbers of families
= 814/1500 = 407/750
(iii) Numbers of families having 2 girls = 211
Probability = Numbers of families having 0 girls/Total numbers of families
= 211/1500
Sum of the probability = 19/60 + 407/750 + 211/1500
= (475 + 814 + 211)/1500 = 1500/1500 = 1
Yes, the sum of these probabilities is 1.

Q.3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

Total numbers of students = 40
Numbers of students = 6
Required probability = 6/40 = 3/20

Q.4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome3 heads2 heads1 headNo head
Frequency23727728

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

Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
Required probability = 72/200 = 9/25

Q.5. 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 ₹)
Vehicles per family
012Above 2
Less than 700010160250
7000-100000305272
10000-130001535291
13000-160002469
5925
16000 or more15798288

Suppose a family is chosen. Find the probability that the family chosen is

(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹7000 per month and does not own any vehicle.
(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.

Total numbers of families = 2400
(i) Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles = 29
Required probability = 29/2400
(ii) Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579
Required probability = 579/2400
(iii) Number of families earning less than ₹7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240

(iv) Number of families earning ₹13000-16000 per month and owning more than 2 vehicles = 25
Required probability = 25/2400 = 1/96
(v) Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579
= 2062
Required probability = 2062/2400 = 1031/1200

Q.6. 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.

MarksNumber of students
0 – 207
20 – 3010
30 – 4010
40 – 5020
50 – 6020
60 – 7015
70 – above8
Total90

Total numbers of students = 90
(i) Numbers of students obtained less than 20% in the mathematics test = 7
Required probability = 7/90
(ii) Numbers of student obtained marks 60 or above = 15+8 = 23
Required probability = 23/90

Q.7. 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.

OpinionNumber of students
like135
dislike65

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

Total numbers of students = 135 + 65 = 200
(i) Numbers of students who like statistics = 135
Required probability = 135/200 = 27/40
(ii) Numbers of students who does not like statistics = 65
Required probability = 65/200 = 13/40

Q.8. Refer to Q.2, 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?

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 3 2 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12
Total numbers of engineers = 40
(i) Numbers of engineers living less than 7 km from her place of work = 9
Required probability = 9/40
(ii) Numbers of engineers living less than 7 km from her place of work = 40 – 9 = 31
Required probability = 31/40
(iii) Numbers of engineers living less than 7 km from her place of work = 0
Required probability = 0/40 = 0

Q.11. 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.

Total numbers of bags = 11
Numbers of bags containing more than 5 kg of flour = 7
Required probability = 7/11

Q.11. 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.

Total numbers of bags = 11
Numbers of bags containing more than 5 kg of flour = 7
Required probability = 7/11

Q.12. In Q.5, 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.
The data obtained for 30 days is as follows:
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

Total numbers of days data recorded = 30 days
Numbers of days in which sulphur dioxide in the interval 0.12-0.16 = 2
Required probability = 2/30 = 1/15

Q.13. In Q.1, 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.
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.

Total numbers of students = 30
Numbers of students having blood group AB = 3
Required probability = 3/30 = 1/10

Maths NCERT solutions class 9 Chapter 15 PROBABILITY