on a quiz there are four multiple - choice questions worth 3 points each and two true/false questions worth…

Answer:

2.8

Explanation:

Step1: Calculate expected value of multiple - choice questions

For each multiple - choice question with 5 choices and 3 points, the probability of getting it right is $p_1=\frac{1}{5}$, and the expected value of one multiple - choice question is $E(X_1)=3\times\frac{1}{5}+0\times(1 - \frac{1}{5})=\frac{3}{5}$. There are 4 multiple - choice questions, so the total expected value of multiple - choice questions is $4\times\frac{3}{5}=\frac{12}{5} = 2.4$.

Step2: Calculate expected value of true/false questions

For each true/false question with 2 choices and 1 point, the probability of getting it right is $p_2=\frac{1}{2}$, and the expected value of one true/false question is $E(X_2)=1\times\frac{1}{2}+0\times(1 - \frac{1}{2})=\frac{1}{2}$. There are 2 true/false questions, so the total expected value of true/false questions is $2\times\frac{1}{2}=1$.

Step3: Calculate total expected value

The total expected value of the score is the sum of the expected values of multiple - choice and true/false questions, $E = 2.4+0.4=2.8$.