You are here
Home > CBSE > NCERT Solutions For Class 9th Maths Chapter 15 : Probability

NCERT Solutions For Class 9th Maths Chapter 15 : Probability

CBSE NCERT Solutions For Class 9th Maths Chapter 15 : Probability. NCERT Solutins For Class 9 Mathematics Probability Exercise 15.1


NCERT Solutions for Class X Maths: Chapter 15 – Probability

Page No: 283

Exercise 15.1

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.

Answer

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

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

Number of girls in a family 2 1
Number 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.

Answer

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.

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

Answer

NCERT Solutions For Class 9th probability

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

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

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

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

ALSO READ:  NCERT Solutions for Class 9th Science Chapter 9 : Force and Laws of Motion

Answer

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

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
1 2 Above 2
Less than 7000 10 160 25
7000-10000 305 27 2
10000-13000 1 535 29 1
13000-16000 2 469 59 25
16000 or more 1 579 82 88
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.

Answer

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
Page No: 2846. 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.

Marks Number of students
0 – 20 7
20 – 30 10
30 – 40 10
40 – 50 20
50 – 60 20
60 – 70 15
70 – above 8
Total 90
AnswerTotal numbers of students = 90

(i) Numbers of students obtained less than 20% in the mathematics test = 7
Required probability = 7/90

ALSO READ:  NCERT Solutions For Class 8th Maths Chapter 3 : Understanding Quadrilaterals

(ii) Numbers of student obtained marks 60 or above = 15+8 = 23
Required probability = 23/90

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.

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.

AnswerTotal 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

8. 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?

Answer

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

Page No: 285

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.

Answer

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

ALSO READ:  NCERT Solutions for Class 6th Civics Chapter 7 : Urban Administration

12. 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.
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

Answer

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

13. 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.
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.

Answer

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

Do You Liked Our Contents? If Yes! Then Please Spare Us Some Time By Commenting Below. Or To Get Daily Minute by Minute Updates On Facebook Twitter and Google+ From Us (Indiashines.in) Please Like Us On Facebook , Follow Us On Twitter and Follow Us On Google+ . If You also Want To Ask Us/Experts Any Questions Then Please Join Our Forum Here and Be Our Exclusive Member.



GO BACK TO CLASS IX MATHS ALL CHAPTERS SOLUTIONS

Indiashines.in
IMPORTANT : All the contents of this website is for educational and informational purpose only. The data is collected from various websites, links, pages spread all over internet and owner self-made.We take utmost care to keep the information on this webpage as complete and accurate as possible but we do not claim our site to be error free. And in no way Indiashines.In will be liable for any losses & damages arises from its contents/text. Indiashines.In in good faith, makes an effort to become a helpful platform for students, jobseekers etc. This website is not endorsed by any Govt. bodies. Before using any information of ours please READ OUR DISCLAIMER.

Leave a Reply

Top