Original practice · fully worked
Original variant: failure probability of a three-component series
A data pipeline works only when each of three independent components works. Their operating probabilities during a run are 0.90, 0.80, and 0.75. Find the probability that the pipeline fails during a run.
- A
0.18 - B
0.25 - C
0.36 - D
0.40 - E
0.46
Answer and calculation
All three components work with probability 0.90×0.80×0.75=0.54. The complementary failure probability is 0.46, choice E.
Setup
Setup
Let W be the event that all three components operate; the pipeline fails on the complementary event.
W=W1∩W2∩W3 Model
Model
Because the component states are independent, multiply their three operating probabilities to obtain Pr(W).
Pr(W)=0.90(0.80)(0.75)=0.54 Compute
Compute
All components operate with probability 0.54, so at least one failure occurs with complementary probability 1-0.54=0.46.
Pr(Wc)=1−0.54=0.46 Answer
Answer
The pipeline failure probability is 0.46, which is choice E.
0.46(E) 