Question

A quiz has multiple-choice questions, each with 5 choices. The answer possibilities are distributed evenly. If a student gets a correct answer they will receive +3 points. If they leave it blank, they will receive 0 points. If they write an incorrect answer, they will receive -1 point. A student guesses the answers to some questions. Determine on average, in the long run, how many points the student will score. (Write your answer as a decimal, with a minus sign if needed.)

Answer 1

The answer is 15 but if they get one wrong then 14 is the answer if i get this wrong i am sorry

Answer 2

Answer:

On an average the number of points that a student will score is:

                                 -0.2

Step-by-step explanation:

The probability of choosing a correct answer = 1/5

( Since out of the 5 choices we have just one correct answer)

The probability of choosing a wrong answer = 4/5

( Since out of the 5 choices only one is correct and 4 are incorrect)

Scores received on correct answer = +3

Scores received on wrong answer = -1

The average scores, in long run will be equal to the expected value. The expected value E, in this case will be:

$E=\dfrac{1}{5}\times 3+\dfrac{4}{5}\times (-1)\\\\E=\dfrac{3}{5}-\dfrac{4}{5}\\\\E=\dfrac{3-4}{5}\\\\E=\dfrac{-1}{5}\\\\E=-0.2$

Thus, in long run, the student will score -0.2 points on average.