5.78 Laundry detergent A manufacturer of laundry detergent has introduced a new product that it claims to be more environmentally sound. An extensive survey gives the percentages shown in the table.

a. Estimate the probability that a randomly chosen consumer would have seen advertising for the new product and tried the product.

b. Given that a randomly chosen consumer has seen the product advertised, estimate the probability that the person has tried the product.

c. Let A be the event that a consumer has tried the product. Let B be the event that a consumer has seen the product advertised. Express the probabilities found in parts a and b in terms of A and B.

d. Are A and B independent? Justify your answer.

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Result of Advertising for New Laundry Product Tried the New Product Advertising Status. Yes No Seen the ad 10% 25% Have not seen ad 5% 60%