5) A soap manufacturer has decided to market two new brands. An analysis of current market conditions and a review of the firm's past successes and failures with new brands have led the manufacturer to believe that the simple events and the probabilities of their occurrence in this marketing experiment are as shown in the table (where S means the brand succeeds and F means the brand fails in the first year). Define the following events: A: {Both new brands are successful in the first year) B: {At least one new brand is successful in the first year} Simple events Probabilities SS 0.09 SF 0.21 FS 0.21 AF 0.49 (a) Find P (A), P (B), P (A ~ B) and P(A B). (Answers: 0.09, 0.51, 0.09, 0.51) (b) Find P (A| B) and P (B | A). (Answers: 0.1765, 1)