A manufacturing facility consists of two production machines: Machine 1 and Mach

Question

A manufacturing facility consists of two production machines: Machine 1 and Machine 2. Each machine manufactures 50% of the product volume. The probability of manufacturing a nonconforming product on Machine 1 and 2 is 10% and 20%, respectively. Moreover, the probability of Machine 1 producing a nonconforming product is independent of the probability of Machine 2 producing a nonconforming product, and vice versa. A manufacturing engineer inspects two consecutive products from one machine. If the manufacturing engineer finds the first product is nonconforming, what is the probability of the second product is also nonconforming?

Explanation / Answer

here probabilty that first product is nonforming =P(1) =P(it is from first m/c and non conforming +it is from second m/c and non conforming) =0.5*0.1+0.5*0.2=0.15

probabilty of both the products non conforming =P(1 & 2) =P(from m/c 1 and both products non conforming +from m/c 2 and both products nonconforming) =0.5*0.1*0.1+0.5*0.2*0.2=0.025

hence probability of second product to be non conforming given 1st is nonconforming =P(2|1)=P(1 &2)/P(1)

=0.025/0.15=0.1667

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