Mathematics

Problem

For two independent events

A

and

B

, it is given that

P(A) = x

P(B) = 2x

, and

P(A\cap B) = 0.18

. a. (i) Find the value of

x

. b. (ii) Verify that the probabilities obtained are valid, i.e. each lies between

0

and

1

, and comment on the consistency of the given data. c. (iii) Calculate

P(A\cup B)