# Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions

Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions Chapter-15. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1, Exe-2, Exe-3, Exe-4, and Chapter Test Questions. Visit official Website for detail information about ISC Board Class-11 Mathematics.

## Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions

 Board ISC Class 11 Subject Mathematics Chapter-15 Probability Session 2024-25 Topics Solutions of ML Aggarwal

### Probability

Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions Chapter-15

• An experiment is said to be a random experiment if there is more than one possible outcome, and it is impossible to predict the outcome in advance.
• All possible results of an experiment are called its outcomes.
• Let us consider an experiment of rolling a die. All possible outcomes are 6, 5, 4, 3, 2, or 1. The set of all these outcomes {6, 5, 4, 3, 2, 1} is known as the sample space and is denoted by ‘S’.
• Let us consider an experiment of tossing Two coins once. Since the coin can turn up Tail or Head,

#### Events in Probability

As defined above, the set of all possible outcomes is known as the Sample space. All elements of a sample space are known as Sample points. An event is a subset of the S (sample space). An empty set is also known as the Impossible event. Event A′ is known as Complementary event A

#### equally likely outcomes

All outcomes with equal probability are called equally likely outcomes. Let S be a finite sample space with equally likely outcomes and A be the event. Therefore, the probability of event A is: P(A) = n(A)/n(S)
Where n(A) = Number of elements on the set A n(S) = Total number of outcomes or the number of elements in the sample space S

#### Axiomatic Approach to Probability

The axiomatic approach is a different way of defining the probability of an event. In this method, some axioms or rules are depicted to indicate possibilities

#### Probability of an event:

For a finite sample space with equally likely outcomes  Probability of an event P(A) = n(A)/n(S)

#### 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

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

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)

### Exe-15.1

Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions Chapter-15

### Exe-15.2

Probability ISC Class-11 Maths  Solutions Chapter-15

### Exe-15.3

Probability ISC Class-11 Solutions Chapter-15

### Exe-15.4

Ch-15 Probability ISC Class-11 Maths Solutions

### Chapter Test

Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions Chapter-15

— End of Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions Chapter-15  :–

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### 7 thoughts on “Probability ISC Class-11 Understanding Maths ML Aggarwal Solutions”

• done all

2. Ch 15 probability not given..only showing the ch 14

• now full chapter PDF showing/ working