Let and be any two events defined on the same sample space.

MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability

Problem

Let

A

and

B

be any two events defined on the same sample space. (i) State the definition of the conditional probability

P(A\mid B)

. (ii) Prove that if

A

and

B

are independent events, then

P(A\mid B)=P(A)

. (iii) A fair die is thrown once. Let

A

be the event that an even number appears and

B

be the event that the number obtained is greater than

3

. Calculate

P(A)

P(B)

and

P(A\cap B)

, and hence verify whether

A

and

B

are independent.