8. An industrial engineer is evaluating the perfo established that at any given

Question

8. An industrial engineer is evaluating the perfo established that at any given time there is a 6% probability of equipment malfunction. The production documentation shows that overall, 4.5% of the products come out defective. The manufacturers documentation shows that given the equipment is functioning normally there is still a 2 producing defectives. Whatis the probablity of the equipment producing defectives given the equipment is malfunctioning? (4 points) rmance of the production equipment. It has been % chance of

Explanation / Answer

P( malfunction ) = 0.06, therefore we get P( normal ) = 1 - 0.06 = 0.94
P( defective ) = 0.045

Also we are given here that:

P( defective | normal ) = 0.02

Now using the law of total probability, we get:

P( defective ) = P( defective | normal )P( normal ) + P( defective | malfunction )P( malfunction )

0.045 = 0.02*0.94 + P( defective | malfunction )*0.06

P( defective | malfunction ) = 0.4367

Therefore 0.4367 is the required probability here.

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