A company has two machines that produce widgets An older mac

A company has two machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces three times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective?

Solution

So for every four widgets, 3 of them will be from the new machine, and 1 of them will be from the old. So our weights are .75 and .25 respectively.

Hence, .75*.08+.25*.23=.1175

that will be the probability that is defective

so the probability that is not defective is 1- 0.1175 =0.8825