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 student's score on the test?
a 1.8
b 5.4
c 3.4.
d 2.8
​

Answer 1

C. 3.4

Explanation:

P(correct MCQ) = ⅕

P(correct T/F) = ½

4×3×⅕ + 2×1×½

2.4 + 1

3.4

Answer 2

C. 3.4

Explanation:

We need to find expected value, which is essentially the value that we expect to get based on the amount of each "thing" at hand.

Here, we have 4 multiple-choice questions worth 3 points each and 2 true/false questions worth 1 point each. Each multiple-choice question has 5 possible answers, so the probability that you get that multiple-choice question correct is 1/5. Similarly, each true/false question has 2 possible answers, so the probability that you get that question right is 1/2.

Expected value, denoted by E(x), has the formula:

E(x) = ∑ xp(x), where x is the number of points you get per problem here and p(x) is the probability of getting the problem correct

E(x) = 4 * 3 * (1/5) + 2 * 1 * (1/2) = 12/5 + 1 = 17/5 = 3.4.

The answer is thus C.