Worked solution · Exam P
This Exam P sample reference tests Mutually Exclusive Events. This problem fills one cell of a two-by-two event partition from its row and column totals. The known intersection forces P(A and D)=0.20, exhausting all of D and leaving P(B and D)=0.00, so choice A.
Independent solution
Setup
Because C and D form a disjoint exhaustive pair, their intersections with A partition event A.
Model
Subtract the supplied A-and-C cell from the A row total to recover the other cell in that row.
Compute
Events A and B also form a disjoint exhaustive pair, so their intersections with D partition event D.
Answer
No probability mass remains in the B-and-D cell.
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Original practice · fully worked
A routing controller sends files through paths R, S, and T with probabilities 0.25, 0.35, and 0.40. The conditional timeout probabilities on paths R and S are 0.10 and 0.30, respectively. The overall timeout probability is 0.28. Calculate the conditional timeout probability on path T.
Paths R and S contribute timeout probabilities 0.025 and 0.105. The remaining joint weight for path T is 0.28-0.025-0.105=0.150, and dividing by T's routing share 0.40 gives 0.375 and choice D.
Setup
Let Q denote a timeout. Multiply each known route share by its conditional timeout probability.
Model
The three routes are mutually exclusive and exhaustive, so their timeout contributions add to the overall timeout probability.
Compute
Recover path T's joint timeout weight, then divide by the probability of using path T.
Answer
The timeout probability conditional on path T is 0.375.
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