probability

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hydraulic landing assemblies coming from an aircraft rework facility are each inspected for defects.
Historical records indicate that 8% have defects in shafts only, 6% have defects in bushing only, and 2% have defects in both shafts and bushing. one of the hydraulic assemblies is selected randomly. What is the probability that the assembly has
a) a bushing defects?
b) a shaft or bushing defect?
c) exactly one of the two types of defects?
d) neither type of defect?

  • probability -

    Let event s represent a Shaft defect and event b represent a Brushing defect.
    The given probabilities are:
    P(s ∩ ¬b) = 0.08
    P(b ∩ ¬s) = 0.06
    P(b ∩ s) = 0.02
    Note: these are mutually exclusive

    What you wish to find are:
    a: Brushing defect.
    P(b) = P(b ∩ ¬s) + P(b ∩ s)

    b: Shaft or Brushing.
    P(s U b) = P(b ∩ ¬s) + P(s ∩ ¬b) + P(b ∩ s)

    c: Shaft and not Brushing OR Brushing and not Shaft
    P((s ∩ ¬b) U (b ∩ ¬s)) = P(s ∩ ¬b) + P(b ∩ ¬s)

    d: Not Shaft and not Brushing
    P(¬s ∩ ¬b) = 1 - P(s U b)

  • probability -

    Good post, Graham

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