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 1 - point multiple - choice questions

For a 1 - point multiple - choice question with 5 choices, the probability of getting it right $p=\frac{1}{5}=0.2$, and the value of getting it right is 1 point and wrong is 0 points. The expected value of one 1 - point multiple - choice question is $E(X_1)=1\times0.2 + 0\times(1 - 0.2)=0.2$. There are 4 such questions, so the total expected value for these questions is $4\times0.2 = 0.8$.

Step2: Calculate expected value of 3 - point multiple - choice questions

For a 3 - point multiple - choice question with 5 choices, the probability of getting it right $p=\frac{1}{5}=0.2$, and the value of getting it right is 3 points and wrong is 0 points. The expected value of one 3 - point multiple - choice question is $E(X_2)=3\times0.2+0\times(1 - 0.2)=0.6$. There are 2 such questions, so the total expected value for these questions is $2\times0.6 = 1.2$.

Step3: Calculate expected value of true/false questions

For a true/false question, the probability of getting it right $p = 0.5$, and the value of getting it right is 1 point and wrong is 0 points. The expected value of one true/false question is $E(X_3)=1\times0.5+0\times(1 - 0.5)=0.5$. There are 2 such questions, so the total expected value for these questions is $2\times0.5 = 1$.

Step4: Calculate total expected value

The total expected value of the score is $0.8 + 1.2+1=2.8$.