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1.Sets, Relation and Functions
12-
Lecture1.1
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Lecture1.2
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Lecture1.3
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Lecture1.4
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Lecture1.5
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Lecture1.6
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Lecture1.7
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Lecture1.8
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Lecture1.9
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Lecture1.10
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Lecture1.11
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Lecture1.12
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2.Trigonometric Functions
28-
Lecture2.1
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Lecture2.2
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Lecture2.3
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Lecture2.4
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Lecture2.5
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Lecture2.6
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Lecture2.7
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Lecture2.8
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Lecture2.9
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Lecture2.10
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Lecture2.11
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Lecture2.12
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Lecture2.13
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Lecture2.14
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Lecture2.15
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Lecture2.16
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Lecture2.17
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Lecture2.18
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Lecture2.19
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Lecture2.20
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Lecture2.21
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Lecture2.22
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Lecture2.23
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Lecture2.24
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Lecture2.25
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Lecture2.26
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Lecture2.27
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Lecture2.28
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3.Mathematical Induction
5-
Lecture3.1
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Lecture3.2
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Lecture3.3
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Lecture3.4
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Lecture3.5
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4.Complex Numbers and Quadratic Equation
15-
Lecture4.1
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Lecture4.2
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Lecture4.3
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Lecture4.4
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Lecture4.5
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Lecture4.6
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Lecture4.7
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Lecture4.8
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Lecture4.9
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Lecture4.10
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Lecture4.11
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Lecture4.12
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Lecture4.13
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Lecture4.14
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Lecture4.15
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5.Linear Inequalities
4-
Lecture5.1
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Lecture5.2
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Lecture5.3
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Lecture5.4
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6.Permutations and Combinations
5-
Lecture6.1
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Lecture6.2
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Lecture6.3
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Lecture6.4
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Lecture6.5
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7.Binomial Theorem
19-
Lecture7.1
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Lecture7.2
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Lecture7.3
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Lecture7.4
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Lecture7.5
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Lecture7.6
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Lecture7.7
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Lecture7.8
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Lecture7.9
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Lecture7.10
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Lecture7.11
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Lecture7.12
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Lecture7.13
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Lecture7.14
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Lecture7.15
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Lecture7.16
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Lecture7.17
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Lecture7.18
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Lecture7.19
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8.Sequences and Series
14-
Lecture8.1
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Lecture8.2
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Lecture8.3
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Lecture8.4
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Lecture8.5
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Lecture8.6
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Lecture8.7
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Lecture8.8
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Lecture8.9
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Lecture8.10
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Lecture8.11
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Lecture8.12
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Lecture8.13
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Lecture8.14
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9.Properties of Triangles
2-
Lecture9.1
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Lecture9.2
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10.Straight Lines
30-
Lecture10.1
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Lecture10.2
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Lecture10.3
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Lecture10.4
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Lecture10.5
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Lecture10.6
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Lecture10.7
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Lecture10.8
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Lecture10.9
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Lecture10.10
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Lecture10.11
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Lecture10.12
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Lecture10.13
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Lecture10.14
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Lecture10.15
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Lecture10.16
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Lecture10.17
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Lecture10.18
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Lecture10.19
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Lecture10.20
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Lecture10.21
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Lecture10.22
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Lecture10.23
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Lecture10.24
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Lecture10.25
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Lecture10.26
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Lecture10.27
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Lecture10.28
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Lecture10.29
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Lecture10.30
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11.Conic Sections
21-
Lecture11.1
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Lecture11.2
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Lecture11.3
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Lecture11.4
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Lecture11.5
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Lecture11.6
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Lecture11.7
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Lecture11.8
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Lecture11.9
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Lecture11.10
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Lecture11.11
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Lecture11.12
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Lecture11.13
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Lecture11.14
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Lecture11.15
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Lecture11.16
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Lecture11.17
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Lecture11.18
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Lecture11.19
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Lecture11.20
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Lecture11.21
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12.Coordinate Geometry
8-
Lecture12.1
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Lecture12.2
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Lecture12.3
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Lecture12.4
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Lecture12.5
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Lecture12.6
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Lecture12.7
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Lecture12.8
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13.Three Dimensional Geometry
3-
Lecture13.1
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Lecture13.2
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Lecture13.3
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14.Limits And Derivatives
12-
Lecture14.1
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Lecture14.2
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Lecture14.3
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Lecture14.4
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Lecture14.5
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Lecture14.6
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Lecture14.7
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Lecture14.8
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Lecture14.9
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Lecture14.10
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Lecture14.11
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Lecture14.12
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15.Mathematical Reasoning
3-
Lecture15.1
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Lecture15.2
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Lecture15.3
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16.Statistics
5-
Lecture16.1
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Lecture16.2
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Lecture16.3
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Lecture16.4
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Lecture16.5
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17.Probability
3-
Lecture17.1
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Lecture17.2
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Lecture17.3
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18.Binary Number
2-
Lecture18.1
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Lecture18.2
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Chapter Notes – Probability
Random Experiment
An experiment whose outcomes cannot be predicted or determined in advance is called a random experiment.
Outcome
A possible result of a random experiment is called its outcome.
Sample Space
A sample space is the set of all possible outcomes of an experiment.
Events
An event is a subset of a sample space associated with a random experiment.
Types of Events
Impossible and sure events: The empty set Φ and the sample space S describes events. Intact Φ is called the impossible event and S i.e. whole sample space is called sure event.
Simple or elementary event: Each outcome of a random experiment is called an elementary event.
Compound events: If an event has more than one outcome is called compound events.
Complementary events: Given an event A, the complement of A is the event consisting of all sample space outcomes that do not correspond to the occurrence of A.
Mutually Exclusive Events
Two events A and B of a sample space S are mutually exclusive if the occurrence of any one of them excludes the occurrence of the other event. Hence, the two events A and B cannot occur simultaneously and thus P(A ∩ B) = 0.
Exhaustive Events
If E1, E2,…….., En are n events of a sample space S and if E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then E1, E2,……… E3 are called exhaustive events.
Mutually Exclusive and Exhaustive Events
If E1, E2,…… En are n events of a sample space S and if
Ei ∩ Ej = Φ for every i ≠ j i.e. Ei and Ej are pairwise disjoint and E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then the events
E1, E2,………, En are called mutually exclusive and exhaustive events.
Probability Function
Let S = (w1, w2,…… wn) be the sample space associated with a random experiment. Then, a function p which assigns every event A ⊂ S to a unique non-negative real number P(A) is called the probability function.
It follows the axioms hold
- 0 ≤ P(wi) ≤ 1 for each Wi ∈ S
- P(S) = 1 i.e. P(w1) + P(w2) + P(w3) + … + P(wn) = 1
- P(A) = ΣP(wi) for any event A containing elementary event wi.
Probability of an Event
If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of occurrence of A is defined as
The odd in favour of occurrence of the event A are defined by m : (n – m).
The odd against the occurrence of A are defined by n – m : m.
The probability of non-occurrence of A is given by P() = 1 – P(A).
Addition Rule of Probabilities
If A and B are two events associated with a random experiment, then
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Similarly, for three events A, B, and C, we have
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) – P(B ∩ C) + P(A ∩ B ∩ C)
Note: If A andB are mutually exclusive events, then
P(A ∪ B) = P(A) + P(B)