Question

On a quiz there are four multiple-choice questions worth 3 points each and two true/talse 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?

Answer 1

Using proportions, it is found that the expected value of the student's score on the test is of 3.4 points.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, there are four multiple choice questions, with five options, worth 3 points each, hence the expected score for the multiple choice questions is given by:

Em(X) = 4 x 1/5 x 3 = 12/5 = 2.4.

There are also two true-false questions(two options), worth 1 points, hence the expected score for the two true-false questions is given by:

Etf(X) = 2 x 1/2 x 1 = 1.

Then, the total expected score is given by:

E(X) = Em(X) + Etf(X) = 2.4 + 1 = 3.4.

More can be learned about proportions at https://brainly.com/question/24372153

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