How Question Count Changes Pass Odds
Here we keep 4 options per question and compare two pass rules: strict (all correct) and moderate (at least 75% correct).
Probability Table (4 Options Per Question)
| Number of Questions (n) | Pass Rule: All Correct | Pass Rule: At Least 75% Correct |
|---|---|---|
| 3 | 1.5625% | 1.5625% |
| 4 | 0.3906% | 5.0781% |
| 5 | 0.0977% | 1.5625% |
| 6 | 0.0244% | 0.4639% |
| 8 | 0.0015% | 0.4227% |
Interpretation
- As n grows, all-correct pass probability falls exponentially.
- A 75% threshold is more forgiving but still declines quickly as quizzes become longer.
- Longer quizzes can improve security, but may also increase false rejects for real users.