OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-18(a), Exe-18(b), Exe-18(c), Exe-18(d), Self Revision and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18

Class: 12th
Subject: Mathematics
Chapter  : Ch-18 Probability  of Section -A
Board ISC
Writer  OP Malhotra, SK Gupta, Anubhuti Gangal
Publications S.Chand Publications 2020-21

-: Included Topics :- 

Exe-18(a)

Exe-18(b)

Exe-18(c)

Exe-18(d)

Self Revision

Chapter Test


OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18

Probability of an Event :-

If a trial result is n exhaustive, mutually exclusive and equally likely cases and m of them are favourable to the happening of an event A, then the probability of happening of A is given by
Probability

Event: A subset of the sample space associated with a random experiment is called an event or a case.
e.g. In tossing a coin, getting either head or tail is an event.

Equally Likely Events :-

The given events are said to be equally likely if none of them is expected to occur in preference to the other.
e.g. In throwing an unbiased die, all the six faces are equally likely to come.

Mutually Exclusive Events: A set of events is said to be mutually exclusive, if the happening of one excludes the happening of the other, i.e. if A and B are mutually exclusive, then (A ∩ B) = Φ
e.g. In throwing a die, all the 6 faces numbered 1 to 6 are mutually exclusive, since if any one of these faces comes, then the possibility of others in the same trial is ruled out.

Exhaustive Events: A set of events is said to be exhaustive if the performance of the experiment always results in the occurrence of at least one of them.
If E1, E2, …, En are exhaustive events, then E1 ∪ E2 ∪……∪ En = S.
e.g. In throwing of two dice, the exhaustive number of cases is 62 = 36. Since any of the numbers 1 to 6 on the first die can be associated with any of the 6 numbers on the other die.

Complement of an Event :-

Let A be an event in a sample space S, then the complement of A is the set of all sample points of the space other than the sample point in A and it is denoted by A’or 𝐴¯.
i.e. A’ = {n : n ∈ S, n ∉ A]

Note:
(i) An operation which results in some well-defined outcomes is called an experiment.
(ii) An experiment in which the outcomes may not be the same even if the experiment is performed in an identical condition is called a random experiment.


Exe-18(a)

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18


Exe-18(b)

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18


Exe-18(c)

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18


Exe-18(d)

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18


Properties of Conditional Probability :-

If E and E are two events of sample space S and G is an event of S which has already occurred such that P(G) ≠ 0, then
(i) P[(E ∪ F)/G] = P(F/G) + P(F/G) – P[(F ∩ F)/G], P(G) ≠ 0
(ii) P[(E ∪ F)/G] = P(F/G) + P(F/G), if E and F are disjoint events.
(iii) P(F’/G) = 1 – P(F/G)
(iv) P(S/E) = P(E/E) = 1

Multiplication Theorem :-

If E and F are two events associated with a sample space S, then the probability of simultaneous occurrence of the events E and F is
P(E ∩ F) = P(E) . P(F/E), where P(F) ≠ 0
or
P(E ∩ F) = P(F) . P(F/F), where P(F) ≠ 0
This result is known as multiplication rule of probability.

Multiplication Theorem for More than Two Events: If F, F and G are three events of sample space, then
Probability Class 12 Notes Maths Chapter 13 4


Self Revision

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18


Chapter Test

OP Malhotra Probability ISC Class-12 Maths Solutions Ch-18

-: End of Probability S. Chand ISC Class-12 Maths Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-12 Maths Solutions


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