Problem

Answer the following questions briefly, justifying each statement wherever necessary. a. (i) Define the union and the intersection of two events

A

and

B

in the context of probability theory. b. (ii) State the rule that relates

P(A\cup B)

P(A)

P(B)

and

P(A\cap B)

for any two events

A

and

B

taken from the same sample space. c. (iii) Using the rule stated in part (ii), show that if the events

A

and

B

are mutually exclusive then

P(A\cup B)=P(A)+P(B)