CHSE Odisha Class 11 Math Notes Chapter 16 Probability

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Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 16 Probability will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 16 Probability

Random Or Statistical Experiment:
A random or statistical experiment is one in which

  • All possible outcomes of the experiment are known in advance.
  • The performance of an experiment result in an outcome is not known in advance.
  • The experiment can be repeated under identical conditions.

Sample Space: Sample space is the set of all possible outcomes of an experiment.

Elementary event. An element of sample space is an elementary event.

Event: An event is a subset of a sample space.

Probability of an event: Probability of an event ‘A’ = \(P(A)=\frac{\text { Size of } A}{\text { Size of } S}\)

Types Of Event:

(a) Impossible event
Φ ⊂ S known as the impossible event P(Φ) = 0

(b) Sure (certain) event:
S ⊂ S known as the sure event. P(S) = 1

(c) Mutually exclusive events:
Two events A and B are mutually, exclusive if A ∩ B = Φ i.e occurence of one excludes the occurence of the other.

(d) Equally likely events:
Two events A and B are equally likely if P(A) = P(B).

(e) Independent events:
Two events are independent if occurence if does not depend on occurence of the other.

(f) Exhaustive events:
The events E1, E2, ….. En are exhaustive if E1 ∪ E2 ….. ∪ En = S.

CHSE Odisha Class 11 Math Notes Chapter 16 Probability

Verbal description of events:
Not a → Ac or \(\overline{\mathrm{A}}\) or A’
A or B (at least one of A or B) → A ∪ B
A and B → A ∩ B
A but not B → A ∩ Bc
Neither A nor B → Ac ∩ Bc = (A ∪ B)c
Exactly one of A, B or C → (A ∩ Bc ∩ Cc) ∪ (Ac ∩ B ∩ Cc) ∪ (Ac ∩ Bc ∩ Cc).
Exactly two of A, B or C → (A ∩ B ∩ Cc) ∪ (A ∩ Bc ∩ C) ∪ (Ac ∩ B ∩ C)

Some Theorems On Probability:

(a) For any event A: 0 ≤ P(A)’ ≤ 1

(b) P(Φ) = 0, P(S) = 1

(c) P(Ac) = 1 – P(A)

(d) For any two events if A ⊆ B then P(A) ≤ P(B).

(e) For any two events A and B. P(A – B) = P(A ∩ Bc) = P(A) – P(A ∩ B)

(f) For any two events A and B P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

(g) If A and B are mutually exclusive then P(A ∪ B) = P(A) + P(B)

(h) For any three events A, B and C P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(B ∩ C) – P(C ∩ A) + P(A ∩ B ∩ C)

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