Question

A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1 (the least expensive), 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 brands 2 and 3 are 20% and 10%, respectively.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

Answer 1

Answer: 60.98%

Step-by-step explanation:

Probability that it is a brand 1 DVD player that needs repair work = Probability of brand 1 DVD needing repairs / Probability that a DVD player will need fixing while under warranty

Probability of brand 1 DVD needing repairs = Brand 1 sales percentage * Percentage of brand 1 needed repair

= 50% * 25%

= 12.5%

Probability that a DVD player will need fixing while under warranty = (50%* 25%) + (30% * 20%) + (20% * 10%)

= 20.5%

Probability that it is a brand 1 DVD player that needs repair work = 12.5% / 20.5%

= 60.98%