Worked solution · Exam P
This Exam P sample reference tests Mutually Exclusive Outcomes. The two complement statements identify the endpoint category probabilities as 0.20 each. Subtracting them from the 0.75 lower-stage total leaves 0.35 for the requested category, choice C.
Independent solution
Setup
Let p_j be the probability of category j, where the five category probabilities sum to one.
Model
Use the two statements that omit one category each to recover those omitted probabilities.
Compute
Subtract the two known category masses from the supplied three-category total.
Answer
The requested category probability is 0.35.
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Error diagnosis
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Original practice · fully worked
Each parcel is assigned to exactly one of four routes: North, East, South, or West. The combined shares for North-or-East, East-or-South, and North-or-South are 0.55, 0.60, and 0.45, respectively, while the West share is 0.20. Determine the East share.
Adding the first two pair totals and subtracting the third leaves twice the East share. Thus 2E=0.55+0.60-0.45=0.70 and E=0.35, choice D.
Setup
Translate the three disjoint-route pair totals into equations.
Model
Combine the equations so the North and South shares cancel.
Compute
Evaluate the resulting one-variable equation.
Answer
The East route receives 35% of parcels.
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