Let and be two events of a sample space with and .

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

Problem

Let

E

and

F

be two events of a sample space

S

with

P(E)\neq0

and

P(F)\neq0

. (i) Define the conditional probability of

E

given

F

. State its mathematical expression. (ii) Starting from the definition obtained in part (i), prove that

P(E\cap F)=P(E)\,P(F|E)

and also that

P(E\cap F)=P(F)\,P(E|F)

. (iii) Using the relations proved in part (ii), write the condition for which the events

E

and

F

are independent. Give a brief justification.