2. A chain of video stores sells three different brand, of TVs. oris TV sales, 5

Question

2. A chain of video stores sells three different brand, of TVs. oris TV sales, 50% are 120 points a. What is the probability that a randomly selected purchaser has purchase a TV that brand A, 30% are brand B, and 20% are year warranty on parts and labor. It is known that 25% of brand A'sTV s require warranty repair work, whereas the correspond respectively brand C. Manufacturer of each brand offers a Le ing percentages for brand B and C are 20% and 10%, will need repair work? b. If a customer returns to the store with a TV that needs a warranty repair work, what is the probability that it is a TV of brand B?

Explanation / Answer

2) P(brand A) = 0.5

P(brand B) = 0.3

P(brand C) = 0.2

P(require warranty | brand A) = 0.25

P(require warranty | brand B) = 0.2

P(require warranty | brand C) = 0.1

a) P(require warranty) = P(require warranty | brand A) * P(brand A) + P(require warranty | brand B) * P(brand B) + P(require warranty | brand C) * P(brand C)

                                    = 0.25 * 0.5 + 0.2 * 0.3 + 0.1 * 0.2

                                    = 0.205

b) P(brand B | require warranty) = P(require warranty | brand B) * P(brand B) / P(require warranty)

                                                    = 0.2 * 0.3 / 0.205

                                                    = 0.2927

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