Question

You are trying to answer a multiple choice question on a standardized test. There are four choices. If you get the question right, you gain one point, and if you get it wrong, you lose 1/3 point. Assume you have no idea what the right answer is, so you pick one of the choices at random. What is the expected value of the number of points you get? What is the expected value of the number of points you get? Round the answer to two decimal places. The expected value of the number of points you get is

Answer 1

Since you have no idea what the right answer is, each choice has a probability of 1/4 of being correct. Let X be the number of points you get.

If you answer correctly, X = 1 with probability 1/4.

If you answer incorrectly, X = -1/3 with probability 3/4.

Thus, the expected value of X is:

E(X) = (1/4)×1 + (3/4)×(-1/3)

E(X) = 1/4 - 1/4

E(X) = 0

Therefore, the expected value of the number of points you get is 0.

Explanation:

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Answer 2

1/3

Explanation: