Question

On a quiz there are four multiple-choice questions worth 3 points each and two true/false questionsworth 1 point each . Each multiple-choice question has five possible choices . If a student randomlyguesses on each question , what is the expected value of the student's score on the test ?

Answer 1

Answer:

The expected value of the student's score on the test is 3.4.

Step-by-step explanation:

Multiple choice questions:

worth 3 points.

Five possible choices, one of which is correct. So the expected value of the student in each multiple choice question is:

$m = 3\frac{1}{5} = 0.6$

True/false questions:

worth 1 point.

2 options, one of which is correct, so the expected value for each is:

$t = 1\frac{1}{2} = 0.5$

What is the expected value of the student's score on the test ?

4 multiple choice, two true-false. So

$E = 4m + 2f = 4(0.6) + 2(0.5) = 2.4 + 1 = 3.4$

The expected value of the student's score on the test is 3.4.