Unit 1 : Probability theory

Question 1

Intersection of sets

Answer 1

All the common elements of given sets

Question 2

Union of sets

Answer 2

All the elements of given sets, no elements should be repeated

Question 3

A - B

Answer 3

All the elements of A that are absent in B

Question 4

B - A

Answer 4

All the elements of B that are absent in A

Question 5

Complement of a set A if S is universal set

Answer 5

Consists of the elements of S that are absent in A

Question 6

De Morgans Laws for any two finite sets

Answer 6

(i) A – (B U C) = (A – B) ∩ (A – C)
(ii) A - (B ∩ C) = (A – B) U (A – C)

De Morgan‘s Laws can also we written as:
(i) (A U B)‘ = A’ ∩ B’
(ii) (A ∩ B)‘ = A’ U B’

Question 7

Given n(A), n(B) and n(AUB). What is n(A ∩ B).

Answer 7

n(A ∩ B) = n(A) + n(B) - n(A ∪ B)

Question 8

Define Probability

Answer 8

A quantitative measure of uncertainty

Question 9

What is Bernoulli trail?

Answer 9

An experiment that has exactly two mutually exclusive possible outcome

Question 10

What is an experiment?

Answer 10

Any procedure that can be infinitely repeated and has a well defined set of possible outcomes

Question 11

Random experiment

Answer 11

An experiment whose outcome can’t be predicted precisely. A single performance of a random experiment is termed as a trail

Question 12

Relative Frequency

Answer 12

Let E be an experiment and A,B be the events associated with E, the the relative frequency of A is defined as n(A)/n where n is the total number of outcomes and n(A) is the number of times event A has occurred

Question 13

Limitation of Relative Frequency

Answer 13

We can’t repeat an experiment indefinitely and thus probability can’t be determined using relative frequency

Question 14

The classical definition

Answer 14

S be the sample space of an event, then the probability of some event is, number of ways event can occur / number of outcomes in S. Provided all elements in S are equally likely

Question 14

The classical definition

Answer 14

S be the sample space of an event, then the probability of some event is, number of ways event can occur / number of outcomes in S. Provided all elements in S are equally likely

Question 15

Limitation of classical definition

Answer 15

If outcomes in S are not equally likely, this is invalid. Using concept of probability while trying to define it

Question 16

Axiom 3

Answer 16

The probability of union of any two set of 2 by 2 incompatible events is sum of probabilities of events. P (A U B U C) = P(A) + P(B) + P(C)

Question 16

Axiom 3

Answer 16

The probability of union of any two set of 2 by 2 incompatible events is sum of probabilities of events. P (A U B U C) = P(A) + P(B) + P(C)