Probability · third 180-minute practice PDF
Exam P Practice Exam III: A Third Full-Length Form
Confirm that your pacing and distribution recognition hold across a third distinct 30-question probability form.
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
Daily renewable output is 200 megawatt-hours on one fifth of days, 500 on one half, and 900 on the remaining three tenths. A storage operator keeps only output above a threshold h between 200 and 500. Choose h so expected stored surplus is 224 megawatt-hours.
- 300 MWh
- 340 MWh
- 350 MWh
- 370 MWh
- 400 MWh
For a threshold between 200 and 500, only the 500 and 900 outcomes contribute. Solving 0.5(500-h)+0.3(900-h)=224 gives h=370.
Setup
Because 200<h<500, the 200-MWh outcome contributes no stored surplus, while the 500- and 900-MWh outcomes contribute 500-h and 900-h.
Model
Weight the two positive surplus amounts by probabilities 0.5 and 0.3 and set their sum equal to the required mean of 224 MWh.
Compute
The expectation simplifies to 520-0.8h. Solving 520-0.8h=224 gives h=370, which lies in the assumed interval.
Answer
Thus the required storage threshold is 370 MWh, corresponding to choice D.
Why the other choices are wrong
- A
- Substituting h=300 gives expected surplus 0.5(200)+0.3(600)=280 MWh, not 224.
- B
- Substituting h=340 gives expected surplus 0.5(160)+0.3(560)=248 MWh, not 224.
- C
- Substituting h=350 gives expected surplus 0.5(150)+0.3(550)=240 MWh, not 224.
- E
- Substituting h=400 gives expected surplus 0.5(100)+0.3(500)=200 MWh, not 224.
Independent answer check
| Primary value | 370 |
|---|---|
| Primary method | Compute the variant by a discrete stop-loss expectation. |
| Independent value | 370 |
| Independent method | At h=370, the three surplus outcomes are 0, 130, and 530; their weighted mean is 0.5(130)+0.3(530)=224. |
| Answer | D · agreement passed |
Contents
Inside the 76-page edition
Candidates preparing in English for the Probability (P) Exam
Table of contents
- A distinct 180-minute practice form
- 30 syllabus-balanced five-choice questions
- Printable answer sheet and answer key
- Complete Setup–Model–Compute–Answer solutions
- Independent verification for every result
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.
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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 III
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76 pages · 30 new practice problems · $39