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
(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
