Half of a set of the parts are manufactured by machine A and half by machine B. Eight percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)

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tutorconsortium33 tutorconsortium33 · Answer 1 · 2022-07-30T13:35:00+02:00

The probability that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.
The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.

To find the probability that a part was manufactured on machine A, given that the part is defective:

The probability that a part was manufactured on machine A given that part is defective:

P ( A | D )

P ( A | D ) = [P (A) * P ( D | A )]/ P ( D )

Where: P (A) is the probability that the part is manufactured in machine A which is 0.2 (half of the parts are manufactured in machine A)

P (D/A) is the probability of a defective part given that the part was manufactured in machine A which is 2% or 0.02

And finally, the probability of defective part in the production is 8% or 0.08 hence :

P ( A | D ) = [ ( 0.2 ) * 0.02 ] / 0.08

P ( A | D ) = 0.024

Therefore, the probability that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.

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