Worked solution · Exam P
This Exam P sample reference tests Contingency Tables. Express the four portfolio cells using one male-nonsmoker count and the unknown female-smoker count. The stated total and row differences reduce to 100=2y, so there are 50 female-smoker policies and choice A.
Independent solution
Setup
Let x be the male-nonsmoker count and y the requested female-smoker count.
Model
Form the male and female portfolio totals from the four cells.
Compute
Apply the stated excess of male policies over female policies and solve.
Answer
The number of female-smoker policies is 50.
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30 original general probability problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
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Original practice · fully worked
A workshop assembles 96 sensor kits, each either standard or premium. A standard kit uses two control chips, while a premium kit uses five. The day's completed kits use 330 control chips in total. Calculate the number of premium kits assembled.
Let S and P be the standard and premium counts. Subtracting twice the total-kit equation from the chip equation leaves 3P=138, so P=46 and choice B.
Setup
Translate the kit and chip totals into two equations.
Model
Remove the two-chip baseline used by every kit.
Compute
The remaining chips are the three-chip premium increments.
Answer
The workshop assembled 46 premium kits.
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