Question

A multiple choice test has 27 questions with four choices each. The examinee gets 3 for each right asnwer and -1 for each wrong answer. If the examinee decided to randonly choose all the asnwers, what is her expecteed score?

A) 0

B) 1

C) 9

D) -3

Answer 1

Probability of correct answer is 1/4 because there is only one correct choice out of four choices

so, probability of incorrect choice = 3/4 because there are 3 incorrect choices for every question.

Mean number of correct choices = sample size*probability = 27*(1/4) = 27*0.25 = 6.75

and total score for 6.75 correct answers is given as

Points on correct answers = number of correct answers*points per answer = 6.75*3 = 20.25

so, he will score 20.25 points on all the correct answer

Similarly

Mean number of incorrect choices = sample size*probability = 27*(3/4) = 27*0.75 = 20.25

and total score for 20.25 incorrect answers is given as

Points on incorrect answers = number of incorrect answers*points per answer = 20.25*(-1) = -20.25

so, he will score -20.25 points on all the incorrect answer

So, the total score on all the questions = point on correct +points on incorrect.

this gives, total score on all the questions =20.25 + (-20.25) = 20.25-20.25 = 0 score

Option A is correct answer