# 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)