Question

You earn 1 point for each correct response on a multiple choice test and lose 0.5 point for each incorrect response. Each question has 4 choices, If a student just guesses, what is the expected value of the guess?

Answer 1

It will be atleast 40%

Answer 2

You earn 1 point for each correct response on a multiple choice test and lose 0.5 point for each incorrect response. Each questions has 4 choices.

The probability that an answer is correct if the Student guesses is $p=\frac{3}{4} =0.75$\\

The probability that an answer is incorrect if the Student guesses is $1-p=1-\frac{3}{4} =0.25$

The expected value of each guess is

$p(1)+(1-p)0.5=0.75+0.25*0.5=0.875\;points$