A workeroperated machine produces a defective item with prob

A worker-operated machine produces a defective item with probability 0.05 if the worker follows the machine\'s operating instructions exactly, and with probability 0.06 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? (Enter your answer to three decimal places.) 050

Solution

Let

D = defective
F = follows the instructions

Then by Bayes\' Rule,

P(D) = P(F) P(D|F) + P(F\')P(D|F\')

= 0.90*(0.05) + (1-0.90)*(0.06)

= 0.051 [ANSWER]