Question 1206331: A worker-operated machine produces a defective item with probability 0.02 if the worker follows the machine's operating instructions exactly, and with probability 0.08 if he does not. If the worker follows the instructions 90% of the time, what proportion of all items produced by the machine will be defective?
Answer by ikleyn(52803)   (Show Source):
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A worker-operated machine produces a defective item with probability 0.02
if the worker follows the machine's operating instructions exactly,
and with probability 0.08 if he does not. If the worker follows the instructions 90% of the time,
what proportion of all items produced by the machine will be defective?
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The probability that the item produced will be defective is
P = 0.9*0.02 + (1-0.9)*0.08 = 0.9*0.02 + 0.1*0.08 = 0.026.
It means that 0.026 of all produced items will be defective,
which is the answer to the problem's question.
Solved.
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