Answer to Question #213067 in Statistics and Probability for Anu

Question

In an entrance examination a student has to 

answer all the 120 questions. Each questions 

has four options and only one option is 

correct. A student gets 1 mark for a correct 

answer and loses 

2

1

 mark for a wrong 

answer. What is the expectation of the mark 

scored by a student if he chooses the answer 

to each questions at random? 

Answer 1

Probability to select correct option $= \frac{1}{4}$

Probability to select incorrect option $= \frac{3}{4}$

Expected marks of 1 question $= \frac{1}{4} \times 1 +\frac{3}{4} \times (- \frac{1}{2}) = - \frac{1}{8}$

Expected marks for 120 questions $= 120 \times (- \frac{1}{8}) = -15 \; marks$