A car manufacturer purchases car batteries from two differen

A car manufacturer purchases car batteries from two different suppliers. Supplier A provides 55% of the batteries and supplier B provides the rest. If 5% of all batteries from supplier A are defective and 4% of the batteries from supplier B are defective. A battery is selected at random. Determine the probability that a randomly selected battery is a) defective b) not defective (question deducted from question a) c) given that the randomly selected battery is defective, find the probability it is from supplier A.

Solution

Let D = defective

hence

a)

P(D) = P(A) P(D|A) + P(B) P(D|B)

= 0.55*0.05 + (1-0.55)*0.04

= 0.0455 [ANSWER]

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b)

P(D\') =1 - P(D) = 0.9545 [ANSWER]

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c)

P(A|D) = P(A)P(D|A)/P(D)

= 0.55*0.05/0.0455

= 0.604395604 [ANSWER]