Multiple Choice Guessing with Partial Knowledge
Model how ruling out wrong options on multiple-choice questions changes your expected score and odds of hitting a target mark — compared with pure random guessing. This is a probability model only, not a guarantee of exam results.
Enter Your Quiz Details
Tell us how many questions are on your multiple-choice quiz, how many options each question has, and how often you can eliminate wrong answers. We'll show how much that partial knowledge changes your odds compared with random guessing.
Questions you're confident you know the answer to (100% correct).
Questions where you can eliminate some wrong options before guessing.
Remaining questions where you'll need to guess randomly.
Tip: Even eliminating one wrong option can significantly improve your odds. On a 4-option question, going from 1/4 (25%) to 1/3 (33%) is a big boost!
Understanding Multiple Choice Odds
How partial knowledge affects your probability of success
How Expected Value Works
Expected value is the average score you would get if you took the same quiz many times. It's calculated by multiplying each outcome by its probability and summing them up:
Expected Score = Σ (questions × P(correct per question))
For example, if you have 5 questions you know (100%), 10 questions where you can eliminate to 50%, and 5 pure guesses at 25%:
Expected = 5×1.0 + 10×0.5 + 5×0.25 = 5 + 5 + 1.25 = 11.25 correct
Why Eliminating Options Helps So Much
4-Option Question
- • No elimination: 1/4 = 25%
- • Eliminate 1: 1/3 ≈ 33% (+8%)
- • Eliminate 2: 1/2 = 50% (+25%)
5-Option Question
- • No elimination: 1/5 = 20%
- • Eliminate 1: 1/4 = 25% (+5%)
- • Eliminate 2: 1/3 ≈ 33% (+13%)
- • Eliminate 3: 1/2 = 50% (+30%)
Even eliminating just one option gives you a meaningful advantage. This is why partial knowledge matters!
Why "Known" Questions Matter Most
Questions you know with certainty (P=100%) contribute their full value to your expected score with zero variance. They "anchor" your score and reduce the randomness of your outcome. The more questions you know outright, the more predictable your final score becomes.
Expected Score vs. Probability Distribution
- Expected Score: The average outcome over many trials. A single number that summarizes your central tendency.
- Probability Distribution: Shows all possible outcomes and their likelihoods. Helps you understand the range of scores you might get.
- Target Probability: The chance of scoring at or above a specific threshold (e.g., 70% to pass).
Important Limitations
- • This is a simplified model—real exams may differ
- • Questions on real exams are often correlated (know one, know related ones)
- • Some wrong answers are designed to trick partial-knowledge students
- • Your self-assessment of knowledge may be imperfect
- • The best strategy is always to study more, not guess better
Frequently Asked Questions
Common questions about the elimination odds model
This calculator uses a simplified probability model that assumes questions are independent, guesses among remaining options are equally likely, and there's no negative marking. Real exams may have correlated questions, trick distractors, or scoring rules that differ from these assumptions. The expected value is an average over many hypothetical attempts—your actual score on any single exam may be higher or lower.
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This tool provides probability estimates for educational insight only. Expected values and probabilities are based on simplified assumptions (independent questions, equal-likelihood guessing, no negative marking). Your actual exam score may differ due to question difficulty, test design, and your true knowledge level. This is not a prediction of your score—use it to understand risk and plan your study strategy.