Sonwil Sporting Goods, producer of the world\'s premier tennis balls, imposes th

Question

Sonwil Sporting Goods, producer of the world's premier tennis balls, imposes the following quality control criteria on it's product: If the bounce is not correct (either too high or too low), or if it has a flaw, in the cover, the ball is rejected. Currently, 12% of all balls produced bounce too high or too low, and 50% of these balls with the incorrect bounce also have cover flaws. Overall, 10% of all balls produced have cover flaws. Find the probability that a randomly selected tennis ball has: (a) (b) (c) both a cover and a bounce defect; a defect; a bounce defect if it has a cover defect; (d) does not have a bounce defect (e) is not defective.

Explanation / Answer

Ans:

Bounce defect=A

Cover flaw=B

Given that

P(A)=0.12

P(B/A)=0.5

P(B)=0.1

a)P(both cover and bounce defect)=P(A and B)=P(B/A)*P(A)=0.5*0.12=0.06

b)P(defect)=P(A or B)=P(A)+P(B)-P(A and B)=0.12+0.1-0.06=0.16

c)P(A/B)=P(A and B)/P(B)=0.06/0.1=0.6

d)P(A')=1-P(A)=1-0.12=0.88

e)P(not defective)=P(neither A nor B)=1-0.16=0.84

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