ML Aggarwal Probability ISC Class-11 Maths Understanding

ML Aggarwal Probability ISC Class-11 Maths Understanding 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.

ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15

Class: 11th
Subject: Mathematics
Chapter  : Ch-15 Probability Section -A of Vol-II
Board ISC
Writer ML Aggarwal
Publications APC Arya Publications 2020-21

-: Select Topics :- 

Exe-15.1,

 Exe-15.2,

 Exe-15.3,

 Exe-15.4,

Chapter Test


ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15

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, . . . . . , Pn are exhaustive and mutually exclusive if P1 ∪ P2 ∪ . . . . . ∪ Pn = S and Ei ∩ Ej = 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

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.


Exe-15.1

ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15


Exe-15.2

ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15


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

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

 

Exe-15.3

ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15


Exe-15.4

ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15


Mutually Exclusive and Exhaustive Events
If E1, E2,…… En are n events of a sample space S and if
Ei ∩ Ej = Φ for every i ≠ j i.e. Ei and Ej are pairwise disjoint and E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then the events
E1, E2,………, En are called mutually exclusive and exhaustive events.

 

Chapter Test

ML Aggarwal Probability ISC Class-11 Maths Understanding Ch-15

-: End of Probability ISC Class-11 ML Aggarwal Maths Understanding Chapter-15 Solution :-

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