Math  /  Data & Statistics

QuestionQuality control: A population of 598 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places. \begin{tabular}{ccc} \hline Lot & Conforming & Nonconforming \\ \hline A & 92 & 11 \\ B & 160 & 32 \\ C & 257 & 46 \\ \hline \end{tabular} Send data to Excel (a) What is the probability that the wafer is from Lot A? (b) What is the probability that the wafer is conforming? (c) What is the probability that the wafer is from Lot AA and Is conforming? (d) Given that the wafer is from Lot AA, what is the probability that it is conforming? (e) Given that the wafer is conforming, what is the probability that it is from Lot A? (f) Let E1E_{1} be the event that the wafer comes from Lot AA, and let E2E_{2} be the event that the wafer is conforming. Are E1E_{1} and E2E_{2} independent?
Part 1 of 6
The probability that the wafer is from Lot A is 0.1722 .
Part 2 of 6
The probability that the wafer is conforming is 0.8502 .
Part 3 of 6
The probability that the wafer is from Lot AA and is conforming is 0.1538 .
Part 4 of 6
The probability that the wafer is conforming given that it is from Lot A is 0.8932 .
Part: 4/64 / 6
Part 5 of 6
The probability that the wafer is from Lot AA given that it is conforming is \square

Studdy Solution
Use the conditional probability formula:
The probability that the wafer is from Lot A given that it is conforming is given by:
P(Lot AConforming)=P(Lot A and Conforming)P(Conforming)P(\text{Lot A} \mid \text{Conforming}) = \frac{P(\text{Lot A and Conforming})}{P(\text{Conforming})}
Given: - P(Lot A and Conforming)=92598=0.1538 P(\text{Lot A and Conforming}) = \frac{92}{598} = 0.1538 - P(Conforming)=509598=0.8502 P(\text{Conforming}) = \frac{509}{598} = 0.8502
Calculate:
P(Lot AConforming)=0.15380.85020.1809P(\text{Lot A} \mid \text{Conforming}) = \frac{0.1538}{0.8502} \approx 0.1809
The probability that the wafer is from Lot A given that it is conforming is approximately:
0.1809 \boxed{0.1809}

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