on a quiz there are four multiple - choice questions worth 3 points each and two true/false questions worth…
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? 1.8 2.8 5.4 3.4
Answer
Answer:
3.4
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 is worth 3 points. There are 4 multiple - choice questions. The expected value of one multiple - choice question is $E(X_1)=3\times\frac{1}{5}=0.6$. For 4 multiple - choice questions, $E(X_{mc}) = 4\times0.6 = 2.4$.
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 is worth 1 point. There are 2 true/false questions. The expected value of one true/false question is $E(X_2)=1\times\frac{1}{2}=0.5$. For 2 true/false questions, $E(X_{tf})=2\times0.5 = 1$.
Step3: Calculate total expected value
The total expected value of the score $E(X)=E(X_{mc})+E(X_{tf})=2.4 + 1=3.4$.