Original practice · fully worked
Original variant: trace a flagged component to its line
A factory's components come from lines A, B, and C in proportions 0.50, 0.30, and 0.20. Their respective automated-flag probabilities are 0.02, 0.04, and 0.10. One component is selected from the flagged stream. Calculate the probability that it came from line C.
- A
0.020 - B
0.100 - C
0.200 - D
0.476 - E
0.667
Answer and calculation
The line-weighted flag contributions are 0.010, 0.012, and 0.020. Line C therefore accounts for 0.020/0.042=10/21=0.4762 of flagged components, so choice D.
Setup
Setup
Let F denote a flag. Multiply each production share by its line-specific flag rate to obtain joint contributions.
Pr(A∩F)=0.50(0.02)=0.010 Pr(B∩F)=0.30(0.04)=0.012 Pr(C∩F)=0.20(0.10)=0.020 Model
Model
The flagged stream is the union of the three mutually exclusive line contributions.
Pr(F)=0.010+0.012+0.020=0.042 Pr(C∣F)=Pr(F)Pr(C∩F) Compute
Compute
Divide line C's flagged contribution by the total flagged contribution.
Pr(C∣F)=0.0420.020=2110=0.4761904762 Answer
Answer
Approximately 47.6% of flagged components came from line C.
0.476(D) 