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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:
Let E be the event of hitting the boundary.

Then, P(E) =

                   = = = 0.2
Probability of not hitting the boundary = 1 – Probability of hitting the boundary
                                                           = 1 – P(E)

                                                           = 1 – 0.2
                                                           = 0.8

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 number of families = 475 + 814 + 211 = 1500

(i) Probability of a family, chosen at random, having 2 girls = =

(ii) Probability of a family, chosen at random, having 1 girl = =

(iii) Probability of a family, chosen at random, having no girl =

                                               Sum of these probabilities =

                                                                                   =

                                                                                   =
                                                                                   
                                                                                   = 1

Hence the sum is checked.

Question-3

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

 


Solution:
Total number of students born in the year = 3 + 4 + 2 + 2 + 5 + 1 + 2 + 6 + 3 + 4 + 4 + 4

                                                           = 40

          Number of students born in August = 6
 

Probability that a student of the class was born in August = =
 

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:
Total number of times the three coins are tossed = 200

              Number of times when 2 heads appear = 72

                   Probability of 2 heads coming up = =

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

  0 1 2 more than 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 owing more than 2 vehicles.
(v) Owning not more than 1 vehicle.
 

Solution:
Total number of families selected = 2400
(i) Number of families earning ` 10000 - 13000 per month and owning exactly
2 vehicles = 29

Probability that the family chosen is earning
` 10000-13000 per month and owning exactly 2 vehicles =


(ii) Number of families earning Rs.16000 or more per month and owning exactly
1 vehicle = 579 Probability that the family chosen is earning
16000 or more per month and owning exactly 1 vehicle = =


(iii) Number of families earning less than ` 7000 per month and does not own any vehicle = 10
Probability that the family chosen is earning less than
` 7000 per month and does not own any vehicle = = .


(iv) Number of families earning ` 13000 - 16000 per month and owning more than 2 vehicles = 25.
Probability that the family chosen is earning
` 13000 -16000 per month and owning more than 2 vehicles = =.


(v) Number of families owning not more than 1 vehicle

      = Number of families owning 0 vehicle + Number of families owning 1 vehicle

      = (10 + 0 + 1 + 2 + 1) + (160 + 305 + 535 + 469 + 579)

      = 14 + 2048 = 2062 Probability that the family chosen owns not more than 1 vehicle = = .

 

Question-6

 In a mathematics test, the marks 90 students of class IX are listed in the table below:
 

Marks
(out of 100)

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.
 
Solution:
Total number of students = 90

(i) Number of students obtaining less than 20% in the mathematics test = 7 Probability that a student obtained less than 20% in mathematics test =


(ii)       Number of students obtaining marks 60 or above = 15 + 8 = 23 Probability that a student obtained marks 60 or above =

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) like statistics, (ii) does not like it.
 
Solution:
Total number of students = 200

(i) Number of students who like statistics = 135

Probability that a student chosen at random likes statistics = =


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

Probability that a student chosen at random does not like it = =

Aliter:

Probability that a student chosen at random does like statistics

              = 1 - probability that a student chosen at random likes statistics

              = 1 - =

 

Question-8

The distance (in km) of 40 female 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:
a. Less than 7 km from her place of work?
b. More than or equal to 7 km from her place of work?
c. Within
 km from her place of work?

Solution:
Total number of female engineers = 40
(a) Number of female engineers whose distance (in km) from their residence to their place of work is less than 7 km = 9. Probability that an engineer lives less than 7 km from her place of work =

(b) Number of female engineers whose distance (in km) from their residence to their place of work is more than or equal to 7 km = 31 Probability that an engineer lives more than or equal to 7 km from her place of residence =
Aliter
 Probability that an engineer lives more than or equal to 7 km from her place of residence
                    = 1 - probability that an engineer lives less than 7 km from her place of work

                    = 1 - =


(c) Number of female engineers whose distance (in km) from their residence to their place of work is within km = 0. Probability that an engineer lives within km from her place of work = = 0.
 

Question-9

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:
Total number of bags of wheat flour = 11, 
Number of bags of wheat flour containing more than 5 kg of flour = 7.


Probability that any of the bags, chosen at random,
               contains more than 5 kg of flour  = .

Question-10

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.
Represent this data in the form of a frequency distribution table.
Use this table to determine the probability that a student of this class, selected random, has blood group AB.

Solution:


Total number of students = 30

Number of students having blood groups AB = 3
Probability that a student of this class, selected at random, has blood group AB = = = 0.1




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