Hydraulic assemblies for landing gear produced by an aircraft rework facility ar

Question

Hydraulic assemblies for landing gear produced by an aircraft rework facility are inspected for defects. History shows that 10% have defects in the shafts, 8% have defects in the bushings, and 2% have defects in both the shafts and the bushings. If one such assembly is randomly chosen, find the probability that it has the following characteristics. only a bushing defect a shaft or bushing defect At least one of the two types of defects only one of the two types of defects no defects in shafts or bushings

Explanation / Answer

Let B denote having bushing defect and S denote having shaft defect.

a. P( B only ) = P( B) - P(B and S) = 8% - 2% = 6%

b. P(B or S) = P(B) + P(S) - P(B and S) = 8% + 10% - 2% = 16%

c. P(At least one of the defects) = P(B or S) = 16%

d. P(only one defect) = P(B or S) - P(B and S) = 16% - 2% = 14%

e. P(no defects) = 1 - P(B or S) = 100% - 16% = 84%

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