
1.Number System
14
Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

Lecture1.7

Lecture1.8

Lecture1.9

Lecture1.10

Lecture1.11

Lecture1.12

Lecture1.13

Lecture1.14


2.Polynomials
10
Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Lecture2.5

Lecture2.6

Lecture2.7

Lecture2.8

Lecture2.9

Lecture2.10


3.Coordinate Geometry
8
Lecture3.1

Lecture3.2

Lecture3.3

Lecture3.4

Lecture3.5

Lecture3.6

Lecture3.7

Lecture3.8


4.Linear Equations
8
Lecture4.1

Lecture4.2

Lecture4.3

Lecture4.4

Lecture4.5

Lecture4.6

Lecture4.7

Lecture4.8


5.Euclid's Geometry
7
Lecture5.1

Lecture5.2

Lecture5.3

Lecture5.4

Lecture5.5

Lecture5.6

Lecture5.7


6.Lines and Angles
10
Lecture6.1

Lecture6.2

Lecture6.3

Lecture6.4

Lecture6.5

Lecture6.6

Lecture6.7

Lecture6.8

Lecture6.9

Lecture6.10


7.Triangles
11
Lecture7.1

Lecture7.2

Lecture7.3

Lecture7.4

Lecture7.5

Lecture7.6

Lecture7.7

Lecture7.8

Lecture7.9

Lecture7.10

Lecture7.11


8.Quadrilaterals
13
Lecture8.1

Lecture8.2

Lecture8.3

Lecture8.4

Lecture8.5

Lecture8.6

Lecture8.7

Lecture8.8

Lecture8.9

Lecture8.10

Lecture8.11

Lecture8.12

Lecture8.13


9.Area of Parallelogram
11
Lecture9.1

Lecture9.2

Lecture9.3

Lecture9.4

Lecture9.5

Lecture9.6

Lecture9.7

Lecture9.8

Lecture9.9

Lecture9.10

Lecture9.11


10.Constructions
7
Lecture10.1

Lecture10.2

Lecture10.3

Lecture10.4

Lecture10.5

Lecture10.6

Lecture10.7


11.Circles
11
Lecture11.1

Lecture11.2

Lecture11.3

Lecture11.4

Lecture11.5

Lecture11.6

Lecture11.7

Lecture11.8

Lecture11.9

Lecture11.10

Lecture11.11


12.Heron's Formula
8
Lecture12.1

Lecture12.2

Lecture12.3

Lecture12.4

Lecture12.5

Lecture12.6

Lecture12.7

Lecture12.8


13.Surface Area and Volume
16
Lecture13.1

Lecture13.2

Lecture13.3

Lecture13.4

Lecture13.5

Lecture13.6

Lecture13.7

Lecture13.8

Lecture13.9

Lecture13.10

Lecture13.11

Lecture13.12

Lecture13.13

Lecture13.14

Lecture13.15

Lecture13.16


14.Statistics
15
Lecture14.1

Lecture14.2

Lecture14.3

Lecture14.4

Lecture14.5

Lecture14.6

Lecture14.7

Lecture14.8

Lecture14.9

Lecture14.10

Lecture14.11

Lecture14.12

Lecture14.13

Lecture14.14

Lecture14.15


15.Probability
8
Lecture15.1

Lecture15.2

Lecture15.3

Lecture15.4

Lecture15.5

Lecture15.6

Lecture15.7

Lecture15.8

NCERT Solutions – Probability Exercise 15.1
Exercise 15.1
Q.1 In a cricket match, batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
Sol.
Since in a cricket match ,a batswoman hits a boundary 6 times out of 30 balls she plays i.e., she missed the boundary 30 – 6 = 24 times out of 30 balls.
Therefore, the probability that a batswoman does not hit a boundary.
=NumberofnothittingaboundaryTotalnumberoftrials(i.e.,balls)
=2430=45
Q.2 1500 families with 2 children were selected randomly, and the following data were recorded :
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.
Sol.
Let E0,E1andE2 be the event of getting no girl, 1girl and 2 girls.
(i) Therefore P(E2) = Probability of a family having 2 girls
=Numberoffamilieshaving2girlsTotalnumberofgirls
=4751500=1960
(ii) Therefore P(E1) = Probability of a family having 1 girl
=Numberoffamilieshaving1girlsTotalnumberoffamilies
=8141500=407750
(iii) Therefore P(E0) = Probability of a family having no girls
=NumberoffamilieshavingnogirlsTotalnumberoffamilies
=2111500
Therefore Sum of probabilities = P(E0)+P(E1)+P(E2)
=2111500+407750+1960
=211+814+4751500=15001500=1
Q.3 Refer to Example 5, section 14.4 Chapter 14. Find the probability that a student of the class was born in August.
Sol.
Clearly from the histograph six students were born in the month of August out of 40 students of a particular section of class – IX.
Probability that a student of the class was born in August
=NumberofstudentsborninAugustTotalnumberofstudents
=640=320
Q.4 Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes :
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Sol.
Since three coins are tossed 200 times, so the total number of trials is 200.
Probability of getting 2 heads
=No.ofoutcomeshaving2headsTotalno.oftrials
=72200
=925
Q.5 An organisation 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 1000013000 per month and owning exactly 2 vehicles.
(ii) earning Rs 16000 or more per month and owning exactly 1 vehicles.
(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
Sol.
The total number of families = 2400
(i) Number of families earning Rs 10000 – 13000 per month and owning exactly 2 vehicles = 29.
Therefore, P (families earning Rs 10000 – 13000 per month and owning exactly 2 vehicles)
=292400
(ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579.
Therefore P (Families earning Rs 16000 or more per month and owning exactly 1 vehicle)
=5792400
=193800
(iii) Number of families earning less than Rs. 7000 per month and does not own any vehicle = 10
Therefore, P (Families earning less than Rs 7000 per month and does not own any vehicle)
=102400=1240
(iv) Number of families earning Rs 13000 – 16000 per month and owning more than 2 vehicles = 25
Therefore, P (Families earning Rs 13000 – 16000 per month and owning more than two vehicles)
=252400=196
(v) Number of families owning not more than 1 vehicle
= Families having no vehicle + Families having 1 vehicle
= (10 + 0 + 1 + 2 + 1) + (160 + 305 + 535 + 469 + 579)
= 14 + 2048 = 2062
P (Families owning not more than 1 vehicle)
=20622400=10311200
Q.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.
Sol.
Total number of students in mathematics is 90.
(i) Clearly, from the given table, the number of student who obtained less than 20% marks in the mathematics test = 7.
P (a student obtaining less than 20% marks) = 790
(ii) Clearly, from the given table, number of students who obtained marks 60 or above.
= (students in 60 – 70) + (students above 70)
= 15 + 8 = 23
Therefore, P (a student obtaining marks 60 and above) = 2390
Q.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.
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it.
Sol.
The total number of students = 200
(i) P (a student likes statistics)
=NumberofstudentswholikestatisticsTotalnumberofstudents
=135200=2740
(ii) P (a student does not like statistics)
=NumberofstudentswhodoesnotlikestatisticsTotalnumberofstudents
=65200=1340
Q.8 Refer to Q.2, Ex 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 12km from her place of work?
Sol.
Total number of engineers = 40
(i) Number of engineers living less than 7 km from their place of work = 9
Therefore P (an engineer lives less than 7 km from her place of work)
=940
(ii) Number of engineers living more than or equal to 7km from her place of work = 31
Therefore P (an engineer lives less than or equal to 7 km from her place of work)
=3140
(iii) Number of engineer lives within 12 km from her place of work = 0
Therefore P (an engineer lives with 12 km from her place of work) = 040=0
Q.9 Activity : Note the frequency of two wheeler, three – wheeler and four – wheeler going past during a time interval, in front of your school gate.
Find the probability that any one vehicle out of the total vehicles you have observed is a two wheeler.
Sol. Activity problem : Collect the data and find the desired probability.
Q.10 Activity : Ask all the students in your class to write a 3digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.
Sol. Activity problem : Do as directed and find the desired probability.
Q.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 5kg of flour.
Sol.
Total number of wheat bags = 11
Number of bags having more than 5 kg = 7
Therefore P(a bag contains more than 5kg ) = 711
Q.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.
Sol.
Total number of days = 30
Concentration of sulphur dioxide in 0.12 – 0.16 on any day = 2
Therefore , required probability =230=115
Q.13 In Q. 1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding the blood group 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.
Sol.
Total number of students = 30
Number of students having blood group AB = 3
Therefore Required probability =330=110