A machine produces defective parts with two different probabilities depending on its state of repair. If...
A machine produces defective parts with two different
probabilities depending on its state of repair.
If the machine is in good working order (G), it produces defective
parts (D) with a 1% chance. If it
needs maintenance, it produces defective parts with a 20% chance.
The probability that the machine is
in good working order is 90%.
(a) What is the probability that the machine produces defective
parts? Draw an appropriate tree
diagram to answer this question.
(b) If it is known that the machine produced defective parts, what
is the probability that the machine
needs maintenance?
Homework Answers
a)
from above
probability that the machine produces defective parts =P(G n D)+P(Gc n D)=0.009+0.02=0.0290
b)
P(Gc|D) =P(D n Gc)/P(D)=0.02/0.029=0.6897
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