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=(3)/(4) =0.75`\\

The probability that an answer is incorrect if the Student guesses is
`1-p=1-(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`