Question

2) 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 bushings only, and 2% have defects in both shafts and bushings. one ot the hydraulic assemblies is selected randomly. What is the probability that the assembly has: (02 Marks) a) Bushing defect? b) Shaft or bushing defect? c) Exactly one of the two types of defects? d) Neither type of defect?

Answer 1

Let S shows the event that defects in shafts, B shows the event that defects in Bushing only. So we have

$P(S \text{ only})=0.08,P(B \text{ only})=0.06,P(B\cap S)=0.02$

a)

The probability that the assembly has Bushing effect is

$P(B)=P(B \text{ only})+P(B\cap S)=0.02+0.06=0.08$

b)

$P(S)=P(S \text{ only})+P(B\cap S)=0.02+0.08=0.10$

By the addition rule we have

$P(B\cup S)=P(B)+P(S)-P(B\cap S)=0.10+0.08-0.02=0.16$

c)

$P(S \text{ only})+P(B \text{ only})=0.08+0.06=0.14$

d)

The probability that there is neither type of defect is

$P\left [(B\cup S)^{c} \right ]=1-P(B\cup S)=1-0.16=0.84$