Today in Statistics, we investigated the following scenario:
A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 13. For each question left unanswered, the score is 4. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?1
I gave students about 20 minutes to tackle this question (along with another probability question) in groups. The following was a humorous exchange I overheard:
Guy: It might be 4 choices…
Girl: Uh… If you can eliminate 4 choices, then you’re not guessing!
Of course, the practical analogy is the SAT, on which students earn 1 point for each correct response, and lose 0.25 points for each incorrect response (while netting zero points for every question they skip).2
Based on the earlier exchange, I felt the need to emphasize:
Yeah, if you can eliminate 4 choices on an SAT question, then you should DEFINITELY answer the question.