A population of 600 semiconductor wafers contain wafers from three lots. The waf

Question

A population of 600 semiconductor wafers contain wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification. The following table presents the number of wafers in each category. A wafer is chosen at random from the population a) If the wafer is from Lot A, what is the probability that it is conforming? b) If the wafer is conforming, what is the probability that it is from Lot A? c) If the wafer is conforming, what is the probability that it is not from Lot C? d) If the wafer is not from Lot C, what is the probability that it is conforming

Explanation / Answer

Ans:

P(conforming)=0.86,P(non conforming)=0.14

P(A)=0.17,P(B)=0.33,P(C)=0.5

a)P(conforming/ A)=P(confirming and A)/P(A)

=0.15/0.17=0.8823

b)P(A/conforming)=P(conforming and A)/P(conforming)=0.15/0.86=0.1744

c)P(not C/conforming)=P(not C and conforming)/P(conforming)=(0.15+0.28)/0.86=0.43/0.86=1/2=0.5

d)P(conforming/not C)=P(conforming and not C)/P(not C)=(0.15+0.28)/(0.17+0.33)=0.43/0.5=0.86

Lot Conforming Non conforming A 88 12 100 B 165 35 200 C 260 40 300 Total 513 87 confirming Non conforming Marginal dist. A 0.15 0.02 0.17 B 0.28 0.06 0.33 C 0.43 0.07 0.50 Marginal dist. 0.86 0.14 1.00

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