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Expected Points from Guessing
0.63
Expected Points from Guessing vs Number of Guesses
Formula
## How to Calculate Guessing Penalty Impact When a test penalizes wrong answers, random guessing has an expected value. ### Formula **Expected Gain = Guesses x (P(correct) x 1 - P(wrong) x Penalty)** Where P(correct) = 1 / Number of Choices If the penalty equals 1/(choices-1), guessing has zero expected value.
Esempio Risolto
A student randomly guesses on 10 questions with 4 choices each and a 0.25 penalty.
- 01P(correct) = 1/4 = 0.25
- 02P(wrong) = 3/4 = 0.75
- 03Expected gain per guess = 0.25 x 1 - 0.75 x 0.25 = 0.25 - 0.1875 = 0.0625
- 04Total expected gain = 10 x 0.0625 = 0.625 points
Domande Frequenti
Should I guess on the SAT?
The current SAT has no guessing penalty, so you should always answer every question. Older SAT versions had a 0.25-point penalty.
When is guessing worth it with a penalty?
If you can eliminate even one choice, guessing becomes more favorable. With 4 choices and 1 eliminated, expected gain per guess rises significantly.
What penalty makes guessing neutral?
A penalty of 1/(choices - 1) makes random guessing have zero expected value. For 4 choices, that is 1/3 or about 0.333.