Question
In: Statistics and Probability
26. A store owner purchases stereos from two companies. From Company A, 450 stereos are purchased...
26. A store owner purchases stereos from two companies. From
Company A, 450 stereos are purchased and 6% are found to be
defective. From Company B, 550 stereos are purchased and 4% are
found to be defective.
a) Given that a stereo is defective, find the probability that
it came from Company A.
b) What is the probability that a product is defective?
Solutions
Expert Solution
Total stereos purchased = 450 + 550 = 1000
P(stereos are purchased from company A) = 450/1000 = 0.45
P(stereos are purchased from company B) = 550/1000 = 0.55
P(defective | company A) = 0.06
P(defective | company B) = 0.04
b) P(defective) = P(defective | company A) * P(company A) + P(defective | company B) * P(company B)
= 0.06 * 0.45 + 0.04 * 0.55
= 0.049
a) P(company A | defective) = P(defective | company A) * P(company A) / P(defective)
= 0.06 * 0.45 / 0.049
= 0.5510
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