Question

The analysis of shafts for a compressor is summarized by conformance to specifications: roundnessconforms yes no surface finish yes 3455 conforms no 1

Analyzing categorical data
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asked 2021-06-25
The analysis of shafts for a compressor is summarized by conformance to specifications: roundnessconforms yes no surface finish yes 3455 conforms no 128
(a) If we know that a shaft conforms to roundness requirements, what is the probability that it conforms to surface finish requirements?
(b) If we know that a shaft does not conform to roundness requirements, what is the probability that it conforms to surface finish requirements?

Answers (1)

2021-06-26

Define events
\(R=\{\text{a shaft meets roundness conformance}\}\)
\(S=\{\text{a shaft meets surface finish conformance}\}\)
(a)We are required to find the probability of S given R. Using the naive definition of conditional probability, it is equal \(P(S|R)=\frac{345}{345+12}=\frac{115}{119} \sim 0.9664\).
(b)We are required to find the probability of S given \(R^{c}\). Using the nauve definition of conditional probability, it is equal to \(P(S|R^{c})=\frac{5}{5+8}=\frac{5}{13} \sim 0.3846\).

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