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 students score on the test? 3.4 2.8 5.4 1.8

Explanation:

Step1: Calculate expected value of multiple - choice questions

The probability of getting a multiple - choice question correct is $p_1=\frac{1}{5}$, and each multiple - choice question is worth 3 points. There are 4 multiple - choice questions. The expected value of one multiple - choice question is $E(X_1)=3\times\frac{1}{5}=\frac{3}{5}$. The expected value of 4 multiple - choice questions is $E_1 = 4\times\frac{3}{5}=\frac{12}{5}=2.4$.

Step2: Calculate expected value of true/false questions

The probability of getting a true/false question correct is $p_2=\frac{1}{2}$, and each true/false question is worth 1 point. There are 2 true/false questions. The expected value of one true/false question is $E(X_2)=1\times\frac{1}{2}=\frac{1}{2}$. The expected value of 2 true/false questions is $E_2=2\times\frac{1}{2} = 1$.

Step3: Calculate total expected value

The total expected value of the score is $E = E_1+E_2$. Substitute $E_1 = 2.4$ and $E_2 = 1$ into the formula, we get $E=2.4 + 1=3.4$.

Answer:

3.4