Class 11 Maths Revision Notes for Probability of Chapter 16 – Free PDF Download

Free PDF download of Class 11 Maths revision notes & short key-notes for Probability of Chapter 16 to score high marks in exams, prepared by expert mathematics teachers from latest edition of CBSE books.

CBSE Class 11 Maths Revision Notes for Probability of Chapter 16

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,…….., E_n are n events of a sample space S and if E₁ ∪ E₂ ∪ E₃ ∪………. ∪ E_n = S, then E₁, E₂,……… E₃ are called exhaustive events.
Mutually Exclusive and Exhaustive Events
If E₁, E₂,…… E_n are n events of a sample space S and if
E_i ∩ E_j = Φ for every i ≠ j i.e. E_i and E_j are pairwise disjoint and E₁ ∪ E₂ ∪ E₃ ∪………. ∪ E_n = S, then the events
E₁, E₂,………, E_n are called mutually exclusive and exhaustive events.
Probability Function
Let S = (w₁, w₂,…… w_n) 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(w_i) ≤ 1 for each W_i ∈ S
• P(S) = 1 i.e. P(w₁) + P(w₂) + P(w₃) + … + P(w_n) = 1
• P(A) = ΣP(w_i) for any event A containing elementary event w_i.

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)