a chain of video Mores sells three different brands of DVD p

a chain of video Mores sells three different brands of DVD players. Of its DVD player sales, 50 percentage are brand 1. 30 percentage are brand 2. and 20 percentage are brand 3. Inch manufacturer offers a l -year warranty on parts and labor. It is known that 25 percentage of brand I s DVD players require warranty repair work, whereas the corresponding percentages for brand 2 and 3 arc 20 percentage and 10 percentage respectively. What is the probability that a randomly selected purchaser has brought a brand 1 DVD player that will need repair while under warranty? What is the probability that a randomly selected purchaser has a DVD player that will need repair while under warranty? If a customer returns to the store with a DVD player that needs warranty repair work, what is the probability that it is a brand 1 DVD player?

Solution

A denotes the event that DVD player of brand 1 is sold. Similarly B for brand 2 and C for brand 3. D denotes the event that DVD player requires repairs.

P(A) = 0.5; P(B) = 0.3 ; P(C) = 0.2; P(D|A) = 0.25 ; P(D|B) = 0.2 ; P(D|C) = 0.1

(a) P(D and A) = P(D|A)P(A) = 0.25x0.5 = 0.125

(b) P(D) = P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C) = 0.205

(c) P(A|D) = P(A and D)/P(D) = P(D|A)P(A)/P(D) = 0.6097