Probability: Class 11 Mathematics NCERT Chapter 16

Key Features of NCERT Material for Class 11 Maths Chapter 16 – Probability

In the last chapter 15, statistics you learned that how to use stats in our day to day life. In this chapter you will learn about Probability and its uses.

Quick revision notes

Random Experiment

An experiment whose outcomes can’t be anticipated or decided ahead of time is known as a random experiment.

Outcome

A potential aftereffect of a random experiment is called its outcome.

Sample Space

A sample space is the arrangement of all potential outcomes of an experiment.

Events

An event is a subset of a sample space related with a random experiment.

Kinds of Events

Impossible and sure events: The unfilled set Φ and the sample space S portrays events. Unblemished Φ is known as the impossible event and S for example entire sample space is called sure event.

Simple or elementary event: Each outcome of a random experiment is called a rudimentary event.

Compound events: Compound events have more than one outcomes.

Complementary events: Given an event A, the supplement of A is the event comprising of all sample space outcomes that don’t relate to the event of A.

Mutually Exclusive Events

Two events A and B of a sample space S are mutually exclusive if the event of any of them rejects the event of the other event. Consequently, the two events An and B can’t happen at the same time and in this manner P(A ∩ B) = 0.

Exhaustive Events

On the off chance that E1, E2,… … .., En are n events of a sample space S and if E1 ∪ E2 ∪ E3 ∪… … . ∪ En = S, at that point E1, E2,… … E3 are called exhaustive events.

Mutually Exclusive and Exhaustive Events

On the off chance that E1, E2,… … En are n events of a sample space S and if

Ei ∩ Ej = Φ for each I ≠ j for example Ei and Ej are pairwise disjoint and E1 ∪ E2 ∪ E3 ∪… … . ∪ En = S, at that point the events

E1, E2,… … , En are called mutually exclusive and exhaustive events.

Probability Function

Let S = (w1, w2,… … wn) be the sample space related with a random experiment. At that point, a function p which appoints each event A ⊂ S to an extraordinary non-negative genuine number P(A) is known as the probability function.

It follows the sayings hold

•       0 ≤ P(wi) ≤ 1 for every Wi ∈ S
•       P(S) = 1 for example P(w1) + P(w2) + P(w3) + … + P(wn) = 1
•       P(A) = ΣP(wi) for any event A containing basic event wi.

Probability of an Event

On the off chance that there are n basic events related with a random experiment and m of them are positive for an event A, at that point the probability of event of An is characterized as

• The odd for event of the event An are characterized by m : (n – m).
• The odd against the event of An are characterized by n – m : m.
•  The probability of non-event of An is given by P( ) = 1 – P(A).

Expansion Rule of Probabilities

On the off chance that A and B are two events related with a random experiment, at that point

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

Likewise, 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 and B are mutually exclusive events, at that point

P(A ∪ B) = P(A) + P(B)