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

Question

A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1, 30% are brand 2, and 20% are brand 3. Each manufacturer offers a 1-year warranty on parts and labor. It is known that 25% of brand 1's DVD players require warranty repair work, whereas the corresponding percentages for brand 2 and 3 are 20% and 10%, respectively. a. What is the probability that a randomly selected purchaser has a DVD player that will need repair work? b. If 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?

Explanation / Answer

All brands, their sale percentages and warranty percentages are shown below.

a. The probability that a randomly selected DVD player will need repair work = Face value of warranty repair

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

= 0.205 or 20.5%

b. Probability that the player needing warranty repair is of brand 1

= (0.5 * 0.25) / 0.205

= 0.61

Brand Brand 1 Brand 2 Brand 3 Sales 50% 30% 20% Warranty repair 25% 20% 10%

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