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jerry7792
18.02.2020 •
Mathematics
A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 30% of the cameras sold have been of the basic model. Of those buying the basic model, 44% purchase an extended warranty, whereas 40% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model?
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Ответ:
the probability is 0.32 (32%)
Step-by-step explanation:
defining the event W= has extended warranty , then
P(W)= probability of purchasing the basic model * probability of purchasing extended warranty given that has purchased the basic model + probability of purchasing the deluxe model * probability of purchasing extended warranty given that has purchased the deluxe model = 0.3 * 0.44 + 0.7 * 0.40 = 0.412
then using the theorem of Bayes for conditional probability and defining the event B= has the basic model , then
P(B/W)= P(B∩W)/P(W)= 0.3 * 0.44/0.412 =0.32 (32%)
where
P(B∩W)= probability of purchasing the basic model and purchasing the extended warranty
P(B/W) = probability of purchasing the basic model given that has purchased the extended warranty
Ответ: