probability / statistics question?

Question

say that you were taking a multiple choice test and the teacher says you only have 30 seconds left. however, you have 5 questions left that you haven't answered. you have no time to even look at them, so you have to guess. would the chances of you getting a better score be higher if you a. filled in every answer as choice B or b. picked a random answer for each question? or would the chances be equal?

Answer 1

Hi Clara,

Let's assume that all answers are equally likely and that there are 4 possible multiple choice answers.

If you choose B, the probability of getting the answer right is 1/4. And the probability of getting all 5 questions correct is (1/4)*(1/4)*(1/4)*(1/4)*(1/4) = 1/1024.

If you choose answers randomly, the probability of getting the answer right is 1/4. And the probability of getting all 5 questions correct is (1/4)*(1/4)*(1/4)*(1/4)*(1/4) = 1/1024.

The probabilities will be the same (I chose 1/4 as an example, but the probabilities will be the same even if we chose a different number)