Answer the following questions related to conditional probability for two events and…

MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

Answer the following questions related to conditional probability for two events

E

and

F

in a sample space

S

with

P(F)\neq 0

. (i) Define the conditional probability of

E

given

F

. (ii) Starting from your definition in part (i), show that

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

. Give a brief justification for each step of your argument. (iii) Explain how the relationship obtained in part (ii) simplifies when

E

and

F

are independent events.