Worked solution · Exam P
This Exam P sample reference tests Independence. Exactly one event occurs in either the E-only or F-only region. Independence gives probabilities 0.294 and 0.104 for those disjoint regions, totaling 0.398, choice B.
Independent solution
Setup
Split the target into the two mutually exclusive ways that exactly one event can occur.
Model
Use independence for each event-complement pair.
Compute
Evaluate the two disjoint probabilities and add them.
Answer
The exactly-one probability is 0.398.
Test the method on unseen problems
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
Two detectors operate independently. Detector A signals with probability 0.25, while detector B signals with unknown probability q. Their outputs agree, meaning both signal or neither signals, with probability 0.60. Calculate q.
Agreement has probability 0.25q+0.75(1-q)=0.75-0.50q. Setting this equal to 0.60 gives q=0.30, choice C.
Setup
Represent agreement as the union of two disjoint matching-output cases.
Model
Independence makes each matching-output probability a product.
Compute
Set the agreement expression equal to the observed probability and solve.
Answer
Detector B signals with probability 0.30.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 192 Exam P general probability practice problems.
Drill the method: Exam P Independence problems
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam P solution in one searchable PDF.
