hydraulic landing assemblies coming from an aircraft rework facility are each inspected for defects.

Question

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?

Answer 1

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)

Answer 2

Good post, Graham

Answer 3

Suppose that an assembly operation in a manufacturing plant involves four steps, which
can be performed in any sequence. If the manufacturer wishes to compare the assembly
time for each of the sequences, how many different sequences will be involved in the
experiment?