Question

On a quiz there are four multiple-choice questions worth 3 points each and two true/false questions worth 1 point each. Each multiple-choice question has five possible choices. If a student randomly guesses on each question, what is the expected value of the student's score on the test?

Answer 1

Answer: 3.4

Step-by-step explanation: if you are taking the Iready test :)

Answer 2

Answer: Expected value would be $\dfrac{17}{5}$

Step-by-step explanation:

Since we have given that

Number of multiple choice question = 4

Number of true false questions = 2

Number of points for each multiple choice question = 3

Number of points for each true false question = 1

Number of choices in multiple choice = 5

Probability of getting correct answer in multiple choice question = $\dfrac{1}{5}$

Probability of getting correct answer in true false question = $\dfrac{1}{2}$

Expected value of the student's score on the test would be

$E(x)=\sum xp(x)\\\\E(x)=4\times 3\times \dfrac{1}{5}+2\times 1\times \dfrac{1}{2}\\\\E(x)=\dfrac{12}{5}+1\\\\E(x)=\dfrac{12+5}{5}=\dfrac{17}{5}$

Hence, expected value would be $\dfrac{17}{5}$