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.


.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.