Question

Elliot is taking a four question multiple choice test. Each question has four possible answers. He is going to completely guess on each question and he will get 5 points for every correct answer and lose two points for every incorrect answer. How many points can he expect to earn on the test (round to the nearest whole number)?


A)
-8


B)
-1


C)
8


D)
20

Answer 1

Let's look at just one question. The questions are independent, so we can just multiply our expected value for 1 question by the number of questions to get the total.

1 question has 4 possible outcomes: 1 right, 3 wrong. Therefore, our probability of guessing correctly is 1/4 or 0.25. Our probability of guessing incorrectly is 3/4, or 0.75. Multiply the probability of guessing correctly by the number of points awarded for guessing correctly (5). Multiply the probability of guessing incorrectly by the number of points awarded for guessing incorrectly (-2). Add the two to get the expected value for one question. Now multiply that by the number of questions to get the total expected value.

Answer 2

-1?

Answer 3

????

Answer 4

E(x) is the expectation for 1 question. 0.25 is the chance of getting a question right, and you gain 5. 0.75 is the chance of getting a question wrong, and you lose 2.

E(x) = 0.25*5 + 0.75*(-2) = ???

Multiply that ??? by the number of questions (four).

Answer 5

-1 looks correct.

Answer 6

thank you