Question

A machine produces parts that are either good $(90\%)$, slightly defective $(2\%)$, or obviously defective $(8\%)$. Produced parts get passed through an automatic inspection machine, which is able to detect any part that is obviously defective and discard it. What is the probability of the parts that make it through the inspection machine and get shipped?

• A. $0.789$
• B. $0.978$
• C. $0.542$
• D. $0.234$

Answer 1

Answer: (B)

Let $G$, $SD$, $OD$ be the events that a randomly chosen shipped part is good, slightly defective, obviously defective respectively.
$\Rightarrow P\left(G\right)=0.90$,
$P\left(SD\right)=0.02$, and $P\left(OD\right)=0.08$
Required probability :
$P\left(G|O{D}^c\right)=\frac{P\left(G\cap O{D}^c\right)}{P\left(O{D}^c\right)}=\frac{P\left(G\right)}{1-P\left(OD\right)}$
$=\frac{.90}{1-.80}=\frac{90}{92}=.978$