Worked solution · Exam P
This Exam P sample reference tests Events and Set Operations. The intersection fixes the first-year count at one and requires the second-year count to be at least one. Exactly statements iii and iv express those two conditions, so the answer is exactly two, choice C.
Independent solution
Setup
Represent the two yearly accident counts by nonnegative integers N1 and N2.
Model
Compare each candidate with both defining restrictions, not merely with a subset of them.
Compute
The remaining statements either demand more than one second-year accident or fail to fix the first-year count.
Answer
Two of the five listed events equal the intersection.
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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.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
Three labeled components are tested once, and each outcome is written as a three-letter P/F string in test order. Let A be the event that the first component passes, and let B be the event that exactly two components pass. Which set of outcome strings is A intersect B?
Event B contains the three strings with exactly two passes. Keeping only those whose first symbol is P leaves PPF and PFP, choice B.
Setup
List the outcomes satisfying the exact-two-pass requirement.
Model
List the outcomes whose first component passes.
Compute
Retain the strings appearing in both sets.
Answer
Exactly two outcome strings satisfy both conditions.
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