Question 1
A screening test for a disease is positive for 95% of people who have it and negative for 90% of people who do not. 2% of the people tested have a disease.
Calculate the probability that a person whose test is positive has a disease.
How to study for Exam P
Exam P rewards practice at pace. Find what you cannot do yet, fix that, and time yourself from the start.
| Pace | Six minutes a question |
|---|---|
| Biggest topic | Univariate random variables, 44 to 50% |
| Start with | The free 48-minute diagnostic |
| Finish with | Full 30-question practice exams |
1. Find your weakest topic
Take the free diagnostic before you plan anything. Eight questions across the three topics show where your time should go, and each wrong answer comes with the reason that option was tempting.
2. Learn each topic by doing
- General probability first: every later topic leans on conditional probability.
- Then univariate random variables, the largest topic. Learn each distribution's story so you can recognize it in a word problem.
- Deductibles and limits get their own time: write down what the insurer pays for each loss before taking any expected value.
- Multivariate last: joint tables, covariance, then sums and the central limit theorem.
3. Practice at exam pace
Once a topic makes sense, switch to timed sets. Six minutes a question sounds generous until an integral goes wrong. Skip, flag and come back, as you will on the day.
4. Sit full practice exams
In the last weeks, sit 30 questions in three hours without notes. Review every miss the same day and redo the topic's practice set for anything you missed twice.
Try 3 questions
Question 2
The lifetime of a pump is exponential with mean 8 years. A pump has already lasted 5 years.
Calculate the probability that it lasts at least 4 more years.
Question 3
For a two-car household, X is the number of auto claims and Y is the number of home claims in a year. The joint probability function of X and Y is:
| X \ Y | 0 | 1 |
|---|---|---|
| 0 | 0.20 | 0.10 |
| 1 | 0.25 | 0.15 |
| 2 | 0.10 | 0.20 |
Calculate .
Next step
Questions people ask
How hard is Exam P?
In SOA's published results, between 43% and 50% of candidates passed each sitting from January 2023 to July 2026.
What should I study first for Exam P?
Conditional probability and Bayes' theorem. They are tested directly and every later topic uses them.
How do I get faster at Exam P questions?
Name the distribution before computing, use the complement for 'at least' questions, and practice in timed sets of five or ten at six minutes a question.