578 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. 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% a. Estimate the probability that a randomly chosen con- sumer would have seen advertising for the new prod- uct 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.
578 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. 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% a. Estimate the probability that a randomly chosen con- sumer would have seen advertising for the new prod- uct 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.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 67E
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Question
Part D
Transcribed Image Text:578 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.
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%
a. Estimate the probability that a randomly chosen con-
sumer would have seen advertising for the new prod-
uct 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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