A factory has 3 injection molding machines. The machines are from different manu

Question

A factory has 3 injection molding machines. The machines are from different manufacturers and have different levels of accuracy. Each machine’s performance is given in the table below:

Percent of Total Parts Produced

Percent of Parts that are Defective and Come from that Machine

Machine A

41%

6%

Machine B

32%

15%

Machine C

27%

4%

a) What is the probability that a randomly selected part came from Machine B?

b) What is the probability that a randomly selected part came from Machine A and is

defective?

c) Given that a part came from Machine C, what is the probability that it is defective?

Percent of Total Parts Produced

Percent of Parts that are Defective and Come from that Machine

Machine A

41%

6%

Machine B

32%

15%

Machine C

27%

4%

Explanation / Answer

answer
the probability that a randomly selected part came from Machine B=0.32

b.
the probability that a randomly selected part came from Machine A and is
defective=P(part came from Machine A)*P(defective)
=0.41*0.06
=0.0246

c.
Given that a part came from Machine C, the probability that it is defective=(P(a part came from Machine C)*P(the probability that it is defective)P(a part came from Machine C)
=(0.27*0.04)(0.27)
=0.04

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