OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution Chapter-22. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-22 (a), 22 (b), Exe-22 (c), Exe-22 (d), Exe-22 (e), Exe-22 (f),  With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Class:	11th
Subject:	Mathematics
Chapter  :	Ch-22 Probability of Section -A

Board	ISC
Writer	OP Malhotra
Publications	S.Chand Publications 2020-21

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–: Select Topics :-

Exe-22 (a)

Exe-22 (b)

Exe-22 (c)

Exe-22 (d)

Exe-22 (e)

Exe-22 (f)

Chapter Test

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OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

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. The event A′ is known as the Complementary event A.

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 an 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

Let P and Q be any two events, then the following formulas can be derived.

• Event P or Q: The set P ∪ Q
• Event P and Q: The set P ∩ Q
• Event P and not Q: The set P – Q
• P and Q are mutually exclusive if P ∩ Q = φ
• Events P₁, P₂, . . . . . , P_n are exhaustive and mutually exclusive if P₁ ∪ P₂ ∪ . . . . . ∪ P_n = S and E_i ∩ E_j = φ for all i ≠ j.

If P and Q are two events, then P(P or Q) = P(P) + P(Q) – P(P and Q), i.e. P(P ∪ Q) = P(P) + P(Q) – P(P ∩ Q)

• If P and Q are mutually exclusive, then P(P or Q) = P(P) + P(Q)
• If M is an event, then P(not M) = 1 – P(M)
• P(sure event) = 1
• P(impossible event) = 0

Random Experiment

An experiment whose outcomes cannot be predicted or determined in advance is called a random experiment.

Outcome
A possible result of a random experiment is called its outcome.

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

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

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.

Probability Function
Let S = (w₁, w₂,…… 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

• 0 ≤ P(w_i) ≤ 1 for each W_i ∈ S
• P(S) = 1 i.e. P(w₁) + P(w₂) + P(w₃) + … + P(w_n) = 1
• P(A) = ΣP(w_i) for any event A containing elementary event w_i.

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Exe-22 (a)

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-10 to 22-11

Question 1:

What do you mean by Random Experiment ? Give two illustrations.  Define sample space associated with a random experiment, give  an example.

Question 2:

…………………..

…………………..

…………………..

Question 12:

Two dies are rolled. A is the event that the sum of the number shown  on the two disc is 5. B is event that at least one of the disc shows up a 3. Are the two events A and B.

(i) …………

(ii) …………

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Exe-22 (b)

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-17 to 22-18

Question 1:

What is the probability of getting

……………

Question 2:

…………………..

…………………..

…………………….

Question 11: 

The ace king, queen, jack  ……………………………. and find the probability that.

(i)……………

(ii)…………

(iii)……….

………………………

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Exe-22 (c)

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-25 to 22-26

Question 1:

A die is thrown once find :

(i)…………..

(ii)…………..

(iii)…………

(iv)…………

(v)……….

(vi)………….

Question 2:

……………..

……………..

…………….

Question 12:

In  a simultaneous t is the probability of getting exactly 3 head ?

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Exe-22 (d)

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-32 to 22-34

Question 1:

Four digit number are formed……………………… at random is an odd number.

Question 2:

…………………..

…………………..

…………………..

Question 22:

Given a group of 4 persons, Find the probability that:

(i) No two  of them have their birthday on the same day.

(ii) All of them have same birthday .

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Exe-22 (e)

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-37

Question 1:

Sammer thrown an ………………… that he throws

(i) 2

(ii) 5

(iii) 2 or 5.

Question 2:

……………………

……………………

……………………

Question 7:

A spinner has numbers and colours on it as shown …………………. of each following cases.

…………………….

…………………….

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Exe-22 (f)

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-45 to 22-47

Question 1:

(i) In a single thrown ……………………………. or both tails.

(ii) A dise is thrown twice …………………… obtain is 5 or 7 !

(iii) Two dice are tossed once …………………….. total of 8.

Question 2:

……………………..

…………………….

……………………..

Question 20:

In a group of student, there are 3 boys and 3 girls. four students are to  be selected at random from …………………………. are selected.

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Chapter Test

OP Malhotra Class-11 Probability S.Chand ISC Maths Solution

Page 22-48

Question 1:

In following two fair dice, what is the …………….. 3 but not exceeding 6.

Question 2:

……………….

………………

………………..

Question 6:

A and B are two events  ………………. determine

(i) ………..

(ii) ………..

(iii) ………..

-: End of Probability Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-11 Maths Solutions

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