Lesson: Probability

Exercise 15.1

Question: 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.

Solution:

Total numbers of balls 30

Numbers of boundaries 6

Numbers of times she didn't hit a boundary 30 − 6 =

24

Probability she did not hit a boundary

24 4

30 5

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.

Solution:

Total numbers of families 475+814+211=1500

(i) Numbers of families having 2 girls 475

Probability of a family having girls

Numbers of families having girls

Total numbers of families

2

2

475 19

1500 60

(ii) Numbers of families having 1 girl 814

Probability of a family having one girl

Numbers of families having girl

Total numbers of families

1

814 407

= =

1500 750

(iii) Numbers of families having 2 girls 211

Probability of a family having no girl

Numbers of families having no girl

Total numbers of families

211

1500

Sum of the probabilities

19 407 211

=

60 750 1500

475 814 211

1500

1500

= = 1

1500

Sum of

Yes, the sum of these probabilities is 1.

Question: 3

Refer to Example 5, Section 14.4 of Chapter 14. Find

the probability that a student of the class was born in

August.

Solution:

Total numbers of students 40

Numbers of students born in august 6

The probability of that a student is born in August

63

40 20

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.

Solution:

Number of times 2 heads came up 72

Number of times the coins were tossed 200

The probability of 2 headscoming up when three coins

are simultaneously tossed

72 9

200 25

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:

Vehicles per family

Monthly

income

(in Rs)

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 `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.

Solution:

Numbers of families 2400

(i) Numbers of families earning `10000 −13000 per

month and owning exactly 2 vehicles 29.

The probability that the family chosen is earning

`10000 – 13000 per month and owning exactly 2

vehicles

29

2400

(ii) Number of families earning `16000 or more per

month and owning exactly 1 vehicle 579.

The probability that the family chosen is earning

` or more per month and owning exactly

vehicle

579

.

2400

(iii) Number of families earning less than `7000 per

month and does not own any vehicle 10

The probability that the family chosen is earning less

than `7000 per month and does not own any vehicle

10 1

2400 240

(iv) Number of families earning

`13000 16000 per month and owning more than 2

vehicles 25

The probability that the family chosen is earning

`13000 16000 per month and owning more than 2

vehicles

25 1

2400 96

(v) Number of families owning not more than 1

vehicle

10 160 0 305 1 535 2 469 1 579

2062

The probability that the family chosen does own not

more than 1 vehicle

2062 1031

2400 1200

Question: 6

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

8

Total

90

Solution:

Numbers of students 90

(i) Numbers of students obtained less than 20% in

mathematics test 7

The probability that a student obtained less than 20%

in the mathematics test

7

90

(ii) Numbers of student obtained marks 60 or above =

15+8 = 23

The probability that a student obtained marks 60 or

above

23

90

Question: 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.

Solution:

Total numbers of student 135 + 65 200

(i) Numbers of students who like statistics 135

The probability that a student chosen at random like

statistics

135 27

200 40

(ii) Numbers of students who does not like statistics

65

The probability that a student chosen at random

does not like statistics

65 13

200 40

Question: 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?

Solution:

The distance (in km) of 40 engineers from their

residence to their place of work as found is given

below:

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

Numbers of engineers 40

(i) Numbers of engineers living less than 7 km from

her place of work 9

The empirical probability that an engineer lives in less

than 7 km from her place of work

9

40

(ii) Numbers of engineers living more than or equal to

7 km from her place of work 40 9 31

The empirical probability that an engineer living more

than or equal to 7 km from her place of work

31

40

(iii) Numbers of engineers living within

1

2

km from

her place of work 0

The empirical probability that an engineer lives

1

2

km

from her place of work

0

0

40

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.

Solution:

Numbers of bags 11

Numbers of bags containing more than 5 kg of flour

7

The probability that any of these bags chosen at

random contains more than 5 kg of flour

7

11

Question: 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

Solution:

Total numbers of days data recorded 30 days

Numbers of days in which concentration of sulphur

dioxide found in the interval 0.12 0.16 = 2

The probability of having the concentration of sulphur

dioxide in the interval 0.12 0.16 on any of these

days

21

30 15

Question: 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

Solution:

Numbers of students 30

Numbers of students having blood group AB = 3

The probability that a student of this class, selected at

random, has blood group AB

31

30 10