Probability · second 180-minute practice PDF
Exam P Practice Exam II: A New 30-Question Rehearsal
Sit a new full-length probability form across general, univariate, and multivariate probability, then trace every error back to its model choice.
One-time USD 39 purchase for a personalized PDF. The 30 original variants are also included in the complete Probability Proof Manual; choose this full-length timed form for curated practice and a lower entry price.
- New practice problems
- 30
- Pages
- 76
- Time limit
- 180 min
- Price
- $39
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One original Exam P practice question with full solution
A load X has density f(x)=2/x³ for x at least 1. Given that X exceeds 2, determine the probability that X also exceeds 3.
- 0.44444
- 0.33333
- 0.25000
- 0.66667
- 0.75000
The survival function is x⁻², so the conditional ratio is (1/9)/(1/4)=4/9, choice A.
Setup
Integrating the density gives a survival function equal to the inverse square of the threshold.
Model
Because exceeding 3 implies exceeding 2, divide the survival probability at 3 by the survival probability at 2.
Compute
The ratio is four ninths, or approximately 0.44444.
Answer
The conditional exceedance probability is approximately 0.44444, selecting choice A.
Why the other choices are wrong
- B
- No standard one-step conditional-tail error was identified that produces 0.33333.
- C
- The value 0.25000 is the unconditional probability of exceeding 2, which is the conditioning probability rather than the conditional ratio.
- D
- No standard one-step conditional-tail error was identified that produces 0.66667.
- E
- No standard one-step conditional-tail error was identified that produces 0.75000.
Independent answer check
| Primary value | 0.4444444444444444 |
|---|---|
| Primary method | Use a Pareto survival ratio. |
| Independent value | 0.4444444444444444 |
| Independent method | Direct integrals over (3,infinity) and (2,infinity) are 1/9 and 1/4. |
| Answer | A · agreement passed |
Contents
Inside the 76-page edition
Candidates preparing in English for the Probability (P) Exam
Table of contents
- 180-minute candidate plan and answer sheet
- 30 syllabus-balanced five-choice questions
- Answer key and complete worked solutions
- 120 concrete wrong-choice analyses
- Two-path verification for every answer
What is included
30 verified original variants selected without duplication for this full-length timed form. Official problem wording is not included.
Verification
Every included result is reproducible
Every selected problem already passed a reproducible calculation, an independent second method, and answer-letter agreement. The compiler rejects any failed check, cross-product duplicate, or official source wording.
Delivery
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Questions about this edition
Are these official sample questions?
No. Every question is an independently written original variant. Official problem wording is not reproduced.
Are complete solutions included?
Yes. Every problem includes Setup, Model, Compute, and Answer steps plus a concrete explanation for each of the four incorrect choices.
How are the answers checked?
Each answer must agree under a reproducible primary calculation and a distinct independent method before the PDF can build.
Does this overlap the complete proof manual?
Yes. These 30 original variants are selected from the verified variant bank included in the Probability Proof Manual. This edition adds a curated full-length timed form, answer sheet, answer key, and focused purchase price.
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ActuaryProof is not affiliated with, endorsed by, or sponsored by the Society of Actuaries. Exam names are used solely to identify the exams for which these study materials are relevant. All problems and solutions are original works.
Probability Practice Examination II
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76 pages · 30 new practice problems · $39