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NCERT solutions Mathematics Class 9 chapter 15 Probability

Chapters

NCERT Mathematics Class 9

Mathematics Textbook for Class 9

Chapter 15 - Probability

Pages 284 - 285

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.

Q 1 | Page 284

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 1.

Q 2 | Page 284

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:-

Find the probability that a student of the class was born in August.

Q 3 | Page 284

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.

Q 4 | Page 284

An organization 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 Rs.)

Vehicles per family
0 1 2 Above 2
Less than 7000 10 160 25 0
7000 – 10000 0 305 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 Rs 10000 − 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 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.

Q 5 | Page 284

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:-

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

(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.

Q 6 | Page 284

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

Q 7 | Page 284

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 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12

What is the empirical probability that an engineer lives:-

(i) less than 7 km from her place of work?What is the empirical probability that an engineer lives:

(ii) more than or equal to 7 km from her place of work?

(iii) within 1/2 km from her place of work?

Q 8 | Page 284

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.

Q 11 | Page 285
Concentration of SO2 (in ppm) Number of days (Frequency)
0.00 − 0.04 4
0.04 − 0.08 9
0.08 − 0.12 9
0.12 − 0.16 2
0.16 − 0.20 4
0.20 − 0.24 2
Total 30

The above frequency distribution table represents 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.

Q 12 | Page 285
Blood Group Number of Students
A 9
B 6
AB 3
O 12
Total 30

The above frequency distribution table represents 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.

Q 13 | Page 285

NCERT Mathematics Class 9

Mathematics Textbook for Class 9
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