Mathematics

Problem

For two events A and B in a probability space it is given that

P(A)=0.4

P(B)=0.5

and

P(A\cup B)=0.7

. a. (i) Find

P(A\cap B)

. b. (ii) Hence compute

P(A\mid B)

. c. (iii) Calculate

P(B\mid A)

. d. (iv) Using any one of the results above, examine whether A and B are independent events, giving full justification.