SOLUTION: A worker operated machine produces a defective item with probability 0.02 if the worker follows the machines operating instructions exactly and with probability 0.04 if he does not

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Question 752429: A worker operated machine produces a defective item with probability 0.02 if the worker follows the machines operating instructions exactly and with probability 0.04 if he does not. If the worker follows the instructions 80% of the time .
a) what proportions of all items produced by the machine will be nondefective.
B)If it is defective, what is the probability that the worker has followed the instruction exactly
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
A worker operated machine produces a defective item with probability 0.02 if the worker follows the machines operating instructions exactly and with probability 0.04 if he does not. If the worker follows the instructions 80% of the time .

a) what proportions of all items produced by the machine will be nondefective.

.8 * .02 = .016
.2 * .04 = .008
total defective = 024
total non-defective = 1 - .024 = .976

B)If it is defective, what is the probability that the worker has followed the instruction exactly.

.016 / .024 = .667

this is how it works as far as i can see.

assume the worker builds 1000 units.
80% of the time the worker follows instructions so the worker is following instructions when the worker builds 800 units.
20% of the time the worker follows instructions so the worker is not following instructions when the worker builds 200 units.

800 units have a defect rate of .02 which leads to 16 defective units.
200 units have a defect rate of .04 which leads to 8 defective units.

there are a total of 24 defective units.
of these, 16 were built following instructions to the letter.
that means 66 and 2/3 percent of the defective units were built following instructions.
the empirical probability that the defective units were built following instructions is therefore .667.