Problem Sets
Never run out of problems. Make the next set from what you're studying.
Upload a chapter. Ritsu maps its knowledge units, forges problems with a crux in each, then works one through with you until it sticks.
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Problem 2 of 18Conditional probability
A positive result on a rare condition
CalculationStretch
A screening test for a condition that affects 1 person in 500 returns a positive result correctly for 98% of people who have the condition, and returns a positive result for 4% of people who do not. One person, chosen at random from the screened population, tests positive. What is the probability that they actually have the condition? Give the value and justify the step that carries the answer.
Tests whether the base rate survives contact with a convincing-looking test statistic.
A few lines of reasoning beats a bare number.
Try first
Try first. Then earn more help.
Help arrives in stages, and every stage is a different kind of help. Press them in order and watch what each one changes about the attempt.
The attempt
The test is right 98% of the time when someone has the condition, so a positive result means there is a 98% chance they have it. The 4% false positive rate makes it slightly lower, so roughly 94%.
Nothing here is locked. You can open the solution first — the tool will let you. The order is the point, not the gate.
A worked solution is useful. Your attempt gives it something to correct.
When the solution arrives first it is easy to confuse “that makes sense” with “I could have produced that.” The attempt opens the gap. The hints let you work inside it. The solution closes it.
You can have the answer. You just have to try first.
Free account · One chapter or document · Your first problem in a couple of minutes
Sound familiar?
Practice problems usually fail in one of two ways. They run out, or they were never yours.
- You finished the question bank with weeks still to go.
- Your professor gave you dense material and almost no practice.
- Your textbook has explanations, and nowhere near enough problems.
- Your course is too specific for a commercial bank to exist.
- You keep searching for “more problems like this one.”
- You read the worked solution, and the next problem still stops you.
- You have plenty of problems — none of them on the material you're graded on.
Finite isn't bad. It just means you eventually need the next set.
Where the problems come from
A question bank
- Written for a standardised exam
- A fixed library
- Runs down as you work
- Ends
Your chapter
- Written from the material you were given
- Mapped into its knowledge units
- Returns to the same units
- Still there tomorrow
When the bank runs out, your material is still there.
The supply
One chapter doesn't have to mean one set.
Don't take it on faith. Look at what comes out of the same chapter three times.
Sourceprobability-ch6.pdf
The knowledge units Ritsu mapped
- Conditional probability
- Random variables
- Expectation & variance
- Common distributions
- Joint & marginal
- Limit theorems
Leans on calculation — the arithmetic of updating a belief.
- A positive result on a rare conditionConditional probability · CalculationStretch
- From outcomes to a distributionRandom variables · CalculationCore
- Expectation of a shifted variableExpectation & variance · CalculationCore
- Recognise the shape from three factsCommon distributions · CalculationWarm-up
- Collapse the joint table to a marginJoint & marginal · CalculationCore
- How many samples before the average settles?Limit theorems · ApplicationCore
Three sets, one chapter — generated from the same units, not drawn from a fixed list.
A fixed bank eventually reaches its last item.
A generated set can come back to the same knowledge structure and build another way to practise it.
And the score follows the units, not the set
Every problem's score rolls up into its unit, and the units into the workbook. That is the map a question bank cannot draw on your material: which idea you can already solve with, and which one is still thin.
Not random
Fresh problems only matter if they're worth solving.
The four stages, in the order the pipeline runs them
- Read the material firstRitsu maps the source into its knowledge units before it writes anything, so a problem can be ordered, targeted and tied to what the document actually covers.
- Use the kinds of problem the source can supportEight families, and the material decides which ones a unit actually gets.
- Skip what the source can't supportIf a chapter cannot carry a real proof problem, no proof problem is manufactured to hit a quota. The instruction to the model is explicit: write fewer for a thin unit.
- Solve it before writing it downThe master works each problem through first, so what ships has a crux worth reaching rather than a number worth plugging.
Fewer real problems beat more filler problems.
The goal isn't infinite random questions. It's an ongoing supply of practice worth doing.
Different jobs
Use the right tool for the right kind of practice.
| What each one does | A commercial question bank | A general chatbot | Problem Sets |
|---|---|---|---|
| Edited by people for one specific exam | Strong | No | No |
| Alignment with a standardised exam | Strong | No | No |
| More problems after you finish the library | No | Sometimes | Yes |
| Built from the document you were given | No | Sometimes | Yes |
| Organised around that document's knowledge units | No | No | Yes |
| Help in stages before the solution | Sometimes | Sometimes | Yes |
| A worked solution | Strong | Yes | Yes |
| Your written attempt, graded | Sometimes | Sometimes | Yes |
If you're preparing for a standardised exam, official and exam-specific practice material is still the right reference. This solves a different problem: what do you practise when you need the next problem, on the exact material in front of you?
Use the bank for exam alignment. Use your material when you need the next problem.
Two ways to work
DIY tells you whether you solved it. Guided finds where the reasoning broke.
DIY (Write & Grade)
One grading pass at the end.
- You write the whole solution
- It comes back graded, with the reasoning read
- Hints if you asked for them
- Then the worked solution
Guided (Socratic)
A round of feedback at every milestone — which is why it costs more per problem than DIY.
- Ritsu solves it privately first
- The problem becomes four to six milestones
- Your reasoning is checked at each one
- You climb rather than submit
- Built from your document, not a topic labelThe units, the problems and the solutions all come from the source you gave it. A problem can quote the line it came from.
- Your best attempt is the one that countsTwo attempts by default. The higher score is the one that moves your mastery, and a retake can never lower it.
- The answer key stays on the serverSolutions, hints and takeaways are never sent to the browser until the run you're in reveals them.
The solution comes last because the attempt is the part that teaches.
Questions
Before you upload anything
It depends on the source and on the problem, and this page won't claim otherwise. What the tool does is read your document into knowledge units first, write a problem only where the material can carry one, and work each problem through before writing it down. Where a unit is thin it writes fewer problems instead of padding.
Ready
Still have material to learn? You still have problems to solve.
Upload the chapter you're actually studying. Ritsu maps it, forges the problems worth solving, and works them through with you. Generate another set when you need more.
Free account · One chapter or document · Your first problem in a couple of minutes
Fresh problems · your material · help before the solution
Your chapter. Your problems. Your attempt first.