Question

When a machine is adjusted properly, 60% of the items produced by it are of high quality and the other 40% are of medium quality. However, the machine is improperly adjusted, 25% of the items produced by it are of high quality and 75% are of medium quality. The machine is improperly adjusted 10% of the time. Suppose that 4 items produced by the machine at a certain time are randomly selected and inspected. If 3 of these iterms are of high qualiy and 1 item is medium quality, what is the probability that the machine was adjusted properly at that time?

Answer 1

Let A is the event machine adjusted properly P(A)= og P (AC) = Ool E is the event 3 out of į items items are high quality Tela) where m.4 2006 P(3 out of 4 art high quality if machine A is there Can be done done using binomial p2 q=ooy -G x pe al 4 x 0-6)xory Pl El A) m24 Binomial where 46 (0.25)? 70.75 P=0-25 920.75

Asking PlAlE) P (Adjusted preoperly given are high quality that Bout of y P(EIA). P(A) plela). P(A) + ? (EIA) PA ex (0.6² xooy xong Gux (0.61? x 0.4x0.9 #yx (0-25)236-75) *0:1) 0.0278 드 0778 +0.00017 0.985
0.985

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