Probability · timed practice PDF
Exam P Practice Exam PDF: 30 Original Questions with Full Solutions
Sit one complete three-hour rehearsal, then review every decision with full solutions and a specific explanation for all 120 wrong choices.
One-time USD 39 purchase for a personalized PDF. All 30 questions are original works; no official problem wording is reproduced.
- New practice problems
- 30
- Pages
- 77
- Time limit
- 180 min
- Price
- $39
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One original Exam P practice question with full solution
A consulting practice must schedule five distinct internal reviews—mortality, morbidity, lapse, expense, and capital—in five consecutive meeting slots. The mortality review must precede the morbidity review, and the lapse and expense reviews may not occupy adjacent slots. How many schedules satisfy both rules?
- 24
- 30
- 36
- 48
- 60
Count schedules that satisfy the precedence rule, then remove those in which lapse and expense are adjacent.
Setup
Exactly half of the 5! unrestricted schedules place mortality before morbidity, so 60 schedules satisfy the precedence rule.
Model
For the prohibited schedules, treat lapse and expense as one block. The block has two internal orders, and symmetry again places mortality before morbidity in half of those arrangements.
Compute
Subtract the 24 prohibited adjacent schedules from the 60 precedence-valid schedules.
Answer
There are 36 schedules satisfying both rules, so the correct choice is C.
Why the other choices are wrong
- A
- Counts the 24 schedules in which lapse and expense are adjacent, which are precisely the schedules that must be excluded.
- B
- Takes half of the 60 precedence-valid schedules without actually counting the nonadjacent lapse-expense placements.
- D
- Subtracts only 12 adjacent schedules, omitting one of the two internal orders of the lapse-expense block.
- E
- Enforces mortality before morbidity but ignores the restriction on adjacent lapse and expense reviews.
Independent answer check
| Primary value | 36 |
|---|---|
| Primary method | Complement count: 5!/2 precedence-valid schedules minus (4! times 2)/2 adjacent schedules. |
| Independent value | 36 |
| Independent method | There are 6 nonadjacent unordered slot pairs for lapse and expense, 2 orders within each pair, and 3!/2 arrangements of the remaining reviews with mortality before morbidity: 6 times 2 times 3 = 36. |
| Answer | C · agreement passed |
Contents
Inside the 77-page edition
Candidates who want a realistic final rehearsal before the Probability (P) Exam
Table of contents
- Candidate instructions and 180-minute timing plan
- 30 original five-choice questions
- Printable answer sheet
- Answer key
- 30 complete Setup–Model–Compute–Answer solutions
- Analysis of all 120 incorrect choices
- Independent verification record for every answer
What is included
30 independently authored questions: 8 General Probability, 14 Univariate Random Variables, and 8 Multivariate Random Variables. No official problem wording is included.
Verification
Every included result is reproducible
Each question records two independently checked calculation paths and matching values; the compiler rejects disagreement. It also checks the final PDF for withheld-source overlap before release.
Delivery
Personal PDF, reusable download
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Before you buy
Questions about this edition
How closely does the exam match the current syllabus?
The 30 questions follow the September 2026 Probability syllabus mix: 8 General Probability, 14 Univariate Random Variables, and 8 Multivariate Random Variables. The problems are original and are not copies or rewrites of official questions.
Are complete solutions included?
Yes. Every problem has a Setup, Model, Compute, and Answer sequence, followed by a specific explanation of why each of the four other choices can arise.
How are the answers checked?
Every answer is reproduced by two independent methods before the compiler accepts it. The delivered edition includes the methods and matching computed values.
Can I print the examination section separately?
Yes. The questions, answer sheet, and answer key appear before the worked solutions, so the examination section can be printed and used without exposing the explanations.
Does the PDF include official sample-question wording?
No. All 30 problem scenarios and parameters were authored for this product. Official problem wording is not reproduced.
How do digital-product refunds work?
Contact contact@fermion.company within 14 days for a delivery failure, unreadable file, duplicate charge, or material mismatch with this description. Change of mind and exam outcome are not refund grounds.
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ActuaryProof is not affiliated with, endorsed by, or sponsored by the Society of Actuaries. "SOA" and exam names are used solely to identify the exams for which these study materials are relevant. All solutions and variant problems are original works.
Probability Practice Examination I
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