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Class 9
Maths :-NCERT Solutions - Probability.

Page No 283:
Question 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 1.

Page No 283:
Question 3:
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.

Page No 283:
Question 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.


Page No 283:
Question 5:
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:

 
  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.

Page No 284:
Question 6:
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 student

0 − 20

20 − 30

30 − 40

40 − 50

50 − 60

60 − 70

70 − above

7

10

10

20

20

15

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.

Page No 284:
Question 8:
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?
(ii) more than or equal to 7 km from her place of work?
(iii) within km from her place of work?

Page No 285:
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 these bags chosen at random contains more than 5 kg of flour.