Class IX Math
NCERT Solution for Probability
NCERT TEXTBOOK QUESTIONS SOLVED
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.
Sol. Here, the total number of trials = 30
Number of times the ball touched boundary = 6
Number of times, the ball missed the boundary = 30 � 6 = 24
Let the event not hitting the boundary be represented by E, then
Thus, the required probability = 0.8
2. 1500 families with 2 children were selected randomly, and the following data were recorded:
Number of girls in a family |
2 |
1 |
0 |
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 I.
Sol: Total number of families = 1500.
(i) Number of families having 2 girls in a family = 475
Probability of family having 2 girls in a family
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE1.JPG)
(ii) Number of families having 1 girl = 814
Probability of family having 1 girl in a family
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE2.JPG)
(iii) Number of families having no girl in a family = 211
Probability of a family having no girl in a family
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE3.JPG)
Now, the sum of the obtained probabilities
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE4.JPG)
i.e., Sum of the above probabilities is 1.
3. Refer to Question 5, Section 14.4, Chapter 14 of NCERT Textbook. Find the probability that a student of the class was born in August.
Sol. From the graph, we have:
Total number of students born in various months in a year = 40
Number of students born in August = 6
Probability of a student of the IX-Class who was born in August
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE5.JPG)
4. Three coins are tossed simultaneously 200 times with the following frequencies of derent 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.
Sol. Total number of times the three coins are tossed = 200
Number of outcomes in which 2 heads coming up = 72
Probability of 2 heads coming up
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE6.JPG)
Thus, the required probability
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE7.JPG)
If the three coins are simultaneously tossed again, then the probability is 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:
Suppose a family is chosen. Find the pmbability that the family chosen is
(i) earning 10000-13000 per month and owning exactly 2 vehicles.
(ii) earning f 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.
Sol. Here, total number of families = 2400
(i) Number of families having earning Rs. 10000 � Rs. 13000 per month and 2 vehicles = 29
Probability of a family (having earning Rs. 10000 � 13000 and 2 vehicles)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE9.JPG)
(ii) Number of families having earning Rs. 16000 or above and owning 1 vehicle = 579
Probability of a family (having earning Rs. 16000 and above and 1 vehicle)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE10.JPG)
(iii) Number of families having earning less than Rs. 7000 and does not own any vehicle = 10
Probability of a family (having earning less than Rs. 7000 and owning no vehicle)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE11.JPG)
(iv) Number of families having earning Rs. 13000 �16000 and owing more than 2 vehicles = 25
Probability of a family (having earning Rs. 13000 � 10000 and owning no vehicle)
(v) Number of families owning not more than 1 vehicle
= [Number of families having no vehicle] + [Number of families having only 1 vehicle]
=[10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579]
= 14 + 2148
= 2162
Probability of a family (owning not more than one vehicle)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE13.JPG)
6. Refer to Table 14.7, Chapter 14 of NCERT Textbook.
(i) Find the probability that a student obtained less than 20% in Mathematics test.
(ii) Find the probability that a student obtained 60 marks or above.
Sol. From the table 14.7, we have:
Marks | Number of students |
0-20 | 7 |
20-30 | 10 |
300 | 10 |
40-50 | 20 |
50-60 | 20 |
60-70 | 15 |
70 and above | 8 |
Total | 90 |
Total number of students = 90
(i) From the given table number of students who have obtained less than 20% marks = 7
Probability of a student (obtaining less than 20% marks)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE14.JPG)
(ii) From the given table, number of students who obtained marks 60% or above
= [Number of students in class-interval 60-70] + [Number of students in the class interval 70 and above]
= 15 + 8 = 23
Probability of a student (who obtained 60 marks and above)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE15.JPG)
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 Dislike | 135 65 |
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it.
Sol. Total number of students whose opinion in obtained = 200
(1) Number of students who like statistics = 135
Probability of a student (who likes statistics)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE16.JPG)
(ii) Number of students who do not like statistics = 65
Probability of a student (who dislike statistics)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE16.JPG)
8. Refer to Q. 2, Exercise 14.2 of NCERT Textbook not 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
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE18.JPG)
km from her place of work?
Sol. Total number of engineers = 40
(i) Number of engineers who are living widen less than 7 km from their work place = 9
Probability of an engineer living within 7 km from work place
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE19.JPG)
(ii) Number of engineers living at a distance more than or equal to 7 km from their work place = 31
Probability of an engineer living at a distance more than or equal to 7 km
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE20.JPG)
(iii) The number of engineers living within
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE18.JPG)
km from their work place = 0
Probability of an engineer who is living within
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE18.JPG)
km from work place
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE21.JPG)
9. 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.
Sol. It is an activity. Students can do it themselves.
10. 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?
Sol. A class room activity for students.
A number is divisible by 3, if the sum of its digits is divisible by 3.
Examples:
(i) Number 45678 is divisible by 3 because 4 + 5 + 6 + 7 + 8 = 30 is divisible by 3
(ii) Number 10786 is not divisible by 3 because 1 + 0 + 7 + 8 + 6 = 22 is not divisible by 3. Question
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 the bags chosen at random contains more than 5 kg of flour.
Sol. Total number of bags = 11
Number of bags having more than 5 kg of flour = 7
Probability of a bag (Having more than 5 kg wheat flour)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE22.JPG)
12. In Q. 5, Exercise 14.2 of NCERT Textbook, 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�V0.16 on any of these days.
Sol. Total number of days = 30
The number of days (on which the sulphur dioxide concentration is in the interval 0.12-0.16) = 2
Probability of a day (on which sulphur dioxide is in 0.12-0.16 interval)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE23.JPG)
13. In Q. 1, Exercise 14.2 of NCERT Textbook, 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.
Sol. Total number of students = 30
Number of students having blood group as AB = 3
Probability of a student (whose blood group is AB)
![](/cbse-ncert/class-9/9-math-Proba-nce-UntitOE24.JPG)