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 CISCE 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 E_{1}, E_{2},…….., E_{n} are n events of a sample space S and if E_{1} ∪ E_{2} ∪ E_{3} ∪………. ∪ E_{n} = S, then E_{1}, E_{2},……… E_{3} are called exhaustive events

**Probability Function: **Let S = (w_{1}, w_{2},…… 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

**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)

**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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