An appliance manufacturer offers extended warranties on its washers and dryers. Based on past sales, the
manufacturer reports that of customers buying both a washer and a dryer, 41% purchase the extended
warranty for the washer, 47% purchase the extended warranty for the dryer, and 56% purchase at least
one of the two extended warranties.
(a) Use the given probability information to set up a hypothetical 1,000 table. (Let W be the event that
the customer purchases an extended warranty for the washer. Let D be the event the customer
purchases an extended warranty for the dryer.)
D Not D Total
W
Not W
Total
(b) Use the table from part (a) to find the following probabilities.
(i) the probability that a randomly selected customer who buys a washer and a dryer purchases an
extended warranty for both the washer and the dryer
(ii) the probability that a randomly selected customer purchases an extended warranty for neither
the washer nor the dryer
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(a) The table can be set up as follows:
D Not D Total
W 410 590 1000
Not W 470 530 1000
Total 880 1120 2000
(b)
(i) The probability that a randomly selected customer who buys a washer and a dryer purchases an extended warranty for both the washer and the dryer can be found by taking the value from the table: 410/2000 = 0.205 or 20.5%.
(ii) The probability that a randomly selected customer purchases an extended warranty for neither the washer nor the dryer can be found by subtracting the probabilities of purchasing at least one warranty from 1: 1 - 0.56 = 0.44 or 44%.
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