How Answer Options Change Success Odds
Holding the quiz length at 3 questions, this table shows how more options per question reduce random authentication success.
Probability Table (3 Questions)
| Options per Question (m) | P(All 3 Correct) | P(At Least 2 Correct) |
|---|---|---|
| 2 | 12.5000% | 50.0000% |
| 3 | 3.7037% | 25.9259% |
| 4 | 1.5625% | 15.6250% |
| 5 | 0.8000% | 10.4000% |
| 6 | 0.4630% | 7.4074% |
Interpretation
- Doubling options from 2 to 4 does not just halve security risk, it compounds across all questions.
- With 3 questions and 4 options each, random all-correct probability is only 1/64.
- Keeping choices broad is one of the simplest ways to harden quiz authentication.