Question

a multiple choice exam has four possible answers for each question. for each correct answer you are award 5 points. for each incorrect answer 2 points are subtracted from your score. for answers left blank no points are added or subtracted.

A) if you do not know the correct answer to a particular question, is it to your advantage to guess. explain

B) if you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? explain

Answer 1

Is the number of questions on the exam given?

Answer 2

no

Answer 3

if you guess the probability you are right is 1/4
if you get it you get 5, if you miss you lose 2
expected values of a guess is
\[5\times \frac{1}{4}-2\times \frac{3}{4}=\frac{5-6}{4}=-\frac{1}{4}\] so you expect to lose one quarter of a point for each guess. so don't guess

Answer 4

for B then you can guess\[5* \frac13-2*\frac23=\frac13\]

Answer 5

This reply summarizes the two above. It comes from another site on the Internet.

a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain.

Answer: Expected points per question if you guess = 5 (1/4) - 2 (3/4) = -1/4
Expected points per question if question left blank = 0
You should not guess since the expected value per question is higher if you do not guess.

b) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain.

Expected points per question if you guess = 5 (1/3) - 2 (2/3) = 1/3
Expected points per question if question left blank = 0
You should guess since the expected value per question is higher if you guess.