Test: Probability And Expected Value By Mathematical Expectation- 1

Physics

Statistics

Mathematics

Economics.

Subjective probability and objective probability

Deductive probability and non–deductive probability

Statistical probability and Mathematical probability

None of these.

Mathematics

Statistics

Management

Accountancy

Can not be predicted

Can be predicted

Can be split into further experiments

Can be selected at random

Complex event

Mixed event

Simple event

Composite event

A  : The student reads in a school. B   : He studies Philosophy.

A  : Raju was born in India. B   : He is a fine Engineer.

A  : Ruma is 16 years old. B  : She is a good singer.

A : Peter is under 15 years of age. B  : Peter is a voter of Kolkata.

A and B are the same events

A and B must be same events

A and B may be different events

A and B are mutually exclusive events

Mutually exclusive

Exhaustive

Equally likely

Independent.

Mutually exclusive events

Equally likely events

Exhaustive events

Dependent events

Mutually exclusive

Exhaustive

Equally likely

All these (a), (b) and (c)

Independent

Dependent

Equally likely

Both (a) and (c)

Independent

Dependent

Not equally likely

Not exhaustiv

A is independent of B

B is independent of A

B is dependent of A

Both (a) and (b)

A and the complement of B are independent

B and the complement of A are independent

Complements of A and B are independent

All of these (a), (b) and (c)

They can be mutually exclusive

They can not be mutually exclusive

They can not be exhaustive

Both (b) and (c)

They are always independent

They may be independent

They can not be independent

They can not be equally likely

Independent

Equally likely

Not equally likely

Both (a) and (b)

– 1 and 1

0 and 1

– 1 and 0

none of these

will never happen

will always happen

may happen

may not happen

symmetric event

dependent event

improbable event

sure event

p/q

p/p+q

q/p+q

none of these

5 : 9

5 : 4

4 : 5

5 : 14

1/3

1

0

any value between 0 and 1

P(A ∩ B) = 1

P(A ∪ B) = 1

P(A ∩ B) = 0

P(A) = P(B)

A is a sure event

B is a sure event

A is not an impossible event

B is an impossible event

B is not a sure event

B is a sure event

B is an impossible event

B is not an impossible event

A and B are equally likely events

A and B are exhaustive events

A and B are mutually exclusive

A and B are mutually independent.

P(A ∪ B) = P(A) + P(B)

P(A ∪ B) = P(A) + P(B) + P(A ∩ B)

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

P(A ∪ B) = P(A) × P(B)

P(A) + P(B) > P(A ∩ B)

P(A) + P(B) < P(A ∩ B)

P(A) + P(B) ≥ P(A∩ B)

P(A) + P(B) ≤ P(A∩ B)

P(A–B) = P(A) – P(B)

P(A–B) = P(A) – P(A ∩ B)

P(A–B) = P(B) – P(A ∩ B)

P(B–A) = P(B) + P(A ∩ B)

it is applicable when the total number of elementary events is finite

it is applicable if the elementary events are equally likely

it is applicable if the elementary events are mutually independent

(a) and (b)

limiting value of the ratio of the no. of times the event A occurs to the number of times the experiment is repeated

the ratio of the frequency of the occurrences of A to the total frequency

the ratio of the frequency of the occurrences of A to the non-occurrence of A

the ratio of the favourable elementary events to A to the total number of elementary events

P(A ∩ B) = P(A) × P(B/A)

P(A ∪ B) = P(A) × P(B/A)

P(A ∪ B) = P(B) + P(B) – P(A ∩ B)

P(A ∩ B) = P(A) × P(B)

P(A) = P(A–B).

P(B) = P(A–B).

P(A) = P(A ∩ B).

P(B) = P(A ∩ B)

P(A) = P(B).

P(A) + P(B) = 1

P(A ∩ B) = 0

P(A ∪ B) = 1

2

3

4

any number

equals to P(A) + P(B)

equals to P(A) × P(B)

equals to P(A) × P(B/A)

equals to P(B) × P(A/B)

always positive numbers.

always positive real numbers.

real numbers.

natural numbers

is always positive

may be positive or negative

may be positive or negative or zero

can never be zero

its expected value is zero

its standard deviation is zero

its standard deviation is positive

its standard deviation is a real number