Single Choice Test

Question

I will have a big exam next week that involves 64 Single-choice questions. There will be two statements of which only one will be correct. I will need to mark only the correct answer. For the correct answer +1 point will be awarded. The wrong answer is a negative point (-1). Not answering the question will result in 0 points. My question is if I can say for sure I can answer at least half of the questions with certainty should I take the 50/50 chance with the remaining of the questions with risking negative points or is not answering anything I am not sure about the smarter choice. Or is it basically the same since it is 50/50 and it should cancel itself out. I am confused how to approach this. Please help.

Thanks

Answer 1

The setup of this test means that you, on average, score a zero on a question where you guess randomly, same as if you leave it blank. This is true regardless of how many questions you answer.

There is a 50/50 chance of getting +1 from a guess, 50/50 chance of getting -1 from a guess.

$$ E[X] =\sum_x xp(x)= (1)(0.5)+(-1)(0.5) =0 $$