Question

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 guesses on each question, what is the expected value of the students score on the

Explanation:

Step1: Calculate expected value of multiple - choice questions

The probability of getting a multiple - choice question correct by guessing is $p=\frac{1}{5}$, and there are 4 multiple - choice questions worth 3 points each. The expected value of one multiple - choice question is $E(X_1)=p\times3+(1 - p)\times0=\frac{1}{5}\times3+\frac{4}{5}\times0 = 0.6$. The total expected value of 4 multiple - choice questions is $4\times0.6 = 2.4$.

Step2: Calculate expected value of true/false questions

The probability of getting a true/false question correct by guessing is $p=\frac{1}{2}$, and there are 2 true/false questions worth 1 point each. The expected value of one true/false question is $E(X_2)=p\times1+(1 - p)\times0=\frac{1}{2}\times1+\frac{1}{2}\times0 = 0.5$. The total expected value of 2 true/false questions is $2\times0.5=1$.

Step3: Calculate total expected score

The total expected score is the sum of the expected values of multiple - choice and true/false questions. So $E = 2.4+1=3.4$.

Answer:

3.4