Probability-NCERT Solutions

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

(ii) Number of families having 1 girl = 814

Probability of family having 1 girl in a family

(iii) Number of families having no girl in a family = 211

Probability of a family having no girl in a family

Now, the sum of the obtained probabilities

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

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

Thus, the required probability

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)

(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)

(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)

(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)

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)

(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)

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)

(ii) Number of students who do not like statistics = 65

Probability of a student (who dislike statistics)

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

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

(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

(iii) The number of engineers living within

km from their work place = 0

Probability of an engineer who is living within

km from work place

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.

REMEMBER

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)

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)

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)