Formula and example
How it is calculated
With k correct guesses: score=known·r+k·r−(guesses−k)·penalty. Correct guesses follow a binomial distribution with p=1/choices.
Worked example
With five known answers and ten guesses from four options, you need at least three correct guesses to reach eight points when correct answers earn one point and wrong answers have no penalty.
Things to check
- Guesses are treated as independent and each answer option as equally likely.
- The expected value is an average over many comparable trials. It does not promise a particular result in one test.
Frequently asked questions
Can guessing lower the expected score?
Yes. The expected contribution of a guess is p·reward−(1−p)·penalty. A large penalty can make this value negative.