The analysis of shafts for a compressor is summarized by conformance t

The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that a shaft is selected at random. What is the probability that the selected shaft conforms to surface finish requirements or to roundness requirements?
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Kevin Hunt
Given,
The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that a shaft is selected at random. Whats the probability that the selected shaft conforms to surface finish requirements orto roundness requirements?

Let us consider,
A be the event of getting shaft that conforms to surface finish requirements.
B be the event of getting shaft that conforms to roundness requirements.
The total number of outcomes, $n\left(S\right)=345+5+12+8=370$
To find P(AUB)
the required formula,
$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$
Calculate the probability,
$P\left(A\cup B\right)=\frac{345+5}{370}+\frac{345+12}{370}-\frac{345}{370}$
$=\frac{350}{370}+\frac{357}{370}-\frac{345}{370}$
$=0.9460+0.9649-0.9324$
$=0.9785$
Therefore, the probability of the shaft conforms to surface finish requirements or to roundness requirements is 0.9785 or $97.85\mathrm{%}$.