Show all of your work and list formulas used 3. A chain of video stores sells th
ID: 3042922 • Letter: S
Question
Show all of your work and list formulas used 3. A chain of video stores sells three different brands of DVD players. Of its DVD players sales, 10% are Brand 1.60 % are Brand 2, and 30% are Brand 3 . Each manufacturer offers a 1-year warranty on parts and labor. It is known that brand 15% of Brand 1 's DVD players require warranty repair work, whereas the corresponding percentages for Brands 2 and 3 are 10% and 20% respectively. a) What is the probability that a randomly selected purchaser has bought a Brand 2 DVD player that will need repair work under warranty? b) If a customer returns to the store with a DVD player that needs warranty repair work what is the probability that it is Brand 2 DVD Player? c) If a customer returns to the store with a DVD player that needs warranty repair work what is the probability that it is Brand 1 DVD Player'?Explanation / Answer
A: Brand 1
B: Brand 2
C: Brand 3
W: Warranty
P(A)= 0.1 ,P(B)=0.6, P(C)=0.3
P(W|A)=0.15, P(W|B)=0.1, P(W|C)=0.2
P(W)=P(W|A)*P(A)+P(W|B)*P(B)+P(W|C)*P(C) =0.15*0.1+0.1*0.6+0.2*0.3=0.135
a) P(W|B)=0.1
b) P(B|W)=P(W|B)*P(B)/P(W)=0.1*0.6/0.135=0.444
c) P(A|W)=P(W|A)*P(A)/P(W)=0.15*0.1/0.135=0.111