Question

You arrive in your history class today only to discover there is a pop quiz! You haven't studied and you aren't at all prepared. Fortunately, the quiz is multiple choice. Each question has five answer choices. You happen to have a die in your pocket. For each question you roll the die and answer A if the die shows 1, B if the die shows 2, etc, leaving the question blank if the die shows a six. For each question you are given one point if you answer it correctly and lose 1/4 point if you answer it incorrectly. You aren't penalized if you leave it blank, you just don't earn a point. What is the expected value for points earned on each question? Enter your answer as a decimal, rounded to two decimal places if necessary

Answer 1

The probability of getting a right answer is 1/6, with a value of 1.

The probability of getting a wrong answer is 4/6 with, a value of -1/4.

The probability of leaving a question empty is 1/6, with a value 0.

The Expected value is


`1* (1)/(6)+( -(1)/(4) )* (1)/(6)+( -(1)/(4) )* (1)/(6)+( -(1)/(4) )* (1)/(6)+( -(1)/(4) )* (1)/(6)+0* (1)/(6)`


`= (1)/(6) +4( -(1)/(4) )* (1)/(6)=(1)/(6)-(1)/(6)=0`