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 1, 30% are brand 2, and 20% are brand 3. It is known that 25% of brand 1's DVD players require repair work, whereas the corresponding percentages for brand 2 and brand 3 are 20% and 10% respectively. 30 points What is the probability that a randomly selected purchaser has bought a brand 1 DVD player and it will need repair work? a. What is the probability that a randomly selected purchaser has a DVD player that will need repair work? b. 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. End

Explanation / Answer

Ans:

P(brand1)=0.5

P(brand2)=0.3

P(brand3)=0.2

P(need repair/brand1)=0.25

P(need repair/brand2)=0.20

P(need repair/brand3)=0.10

a)P(need repair/brand1)=0.25

P(brand1 and need repair)/P(brand 1)=0.25

P(brand 1 and need repair)=0.25*0.5=0.125

b)P(need repair)=P(need repair/brand1)*P(brand1)+P(need repair/brand2)*P(brand2)+P(need repair/brand3)*P(brand3)

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

=0.125+0.06+0.02

=0.205

c)P(brand1/need repair)=P(need repair/brand1)*P(brand 1)/P(need repair)

=0.25*0.5/0.205

=0.125/0.205

=0.6098

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