3. A chain of video stores sells three different brands of DVD players. Of its D

Question

3. A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand i, 30% are brand 2, and 20% are brand 3. It is known that 25% of brand 1's DVD players require a repair work, whereas the corresponding percentages for brand 2 and 3 are 20% and 10%, respectively. What is the probability that a randomly selected purchaser has brought a brand 1 DVD player that will need a repair work? a. b. What is the probability that a randomly selected purchaser has a DVD player that will need a repair work? If a customer returns to the store with a DVD player that needs repair work, what is the probability that it is a brand 1 DVD player? c.

Explanation / Answer

P(D1) = 0.5, P(D2) = 0.3, P(D3) = 0.2

P(R|D1) = 0.25, P(R|D2) = 0.1, P(R|D3) = 0.1

(A)
Required probability, P(D1 and R) = P(D1) * P(R|D1) = 0.5 * 0.25 = 0.125

(B)
Required probability, P(R) = P(D1 and R) + P(D2 and R) + P(D3 and R) = 0.5*0.25 + 0.3*0.1 + 0.2*0.1 = 0.175

(C)
P(D1|R) = P(D1 and R)/P(R) = 0.125/0.175 = 0.7143

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