A pool exists so a retake is not the same quiz. Drawing ten from fifteen means the second attempt repeats about two thirds of the first, which is not what anybody intended. Enter your pool, draw and attempt count and see the repeat rate, the chance of any repeat, and how much of the pool a learner will have seen.
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A retake repeats about 67% of the questions. The pool is doing very little. A learner who fails and retakes is largely answering the same quiz, which is the situation pooling exists to prevent.
To hold repeats to a quarter of the draw, the pool needs about 40 questions at this draw size. That is a real amount of writing, which is worth knowing before the pool is promised to anybody.
After 3 attempts a learner will have seen about 96% of the pool. At that point the pool is effectively exhausted, and a further attempt is a memory test rather than an assessment.
| Pool size | Repeated on a retake | Seen after all attempts |
|---|---|---|
| 15yours | 67% | 96% |
| 23 | 43% | 82% |
| 30 | 33% | 70% |
| 45 | 22% | 53% |
| 60 | 17% | 42% |
These are exact figures rather than a simulation. The share repeated on a retake is the draw size divided by the pool size, which is why doubling the pool halves it, and why a pool only slightly larger than the draw achieves almost nothing.
Works out what a question pool actually achieves: how much of a retake repeats, the chance of any repeat at all, and how much of the pool a learner will have seen by their last attempt.
A pool exists so that a learner retaking a quiz is not answering the same questions. Whether it succeeds is a probability question, and the answer is usually worse than assumed. Ten drawn from a pool of fifteen repeats about two thirds of the previous attempt, and cannot avoid repeating at all, because only five questions are left over.
The share of a retake that repeats is simply the draw size divided by the pool size. Doubling the pool halves the repeats. A pool only slightly larger than the draw achieves almost nothing, which is the shape most pools are in, because writing questions is the expensive part and fifteen feels like a lot when you have just written them.
These are exact figures rather than a simulation, and they assume every question is equally likely to be drawn. If your authoring tool weights questions or draws from several sub-pools, the real numbers will differ, though never in a direction that makes a small pool adequate.