This Exam P sample reference tests Independence. If the smaller marginal is q, independence gives 2q²=0.15. The complementary product is 0.32842, so choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
DThe value 0.67 is the probability of at least one event, 1-0.328416, rounded. It is the complement of the requested neither-event probability.
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
Variant answer in brief
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.
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
