Question

You are trying to answer a multiple choice question on a standardized test. There are five choices. If you get the question right, you gain one point, and if you get it wrong, you lose 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?

Answer 1

Answer: -0.6

Step-by-step explanation:

Given : The number choices to a question : 5

Let we have no idea what the right answer is, so you pick one of the choices at random.

The probability that the answer is correct : $P(x)=\dfrac{1}{5}=0.2$

Then , the probability of the answer is not correct : $P(x')=1-0.2=0.8$

Then , the expected value of the number of points you get :-

$E(x)=P(x)\times\text{Points on x}+P(x')\times\text{Points on x'}\\\\\Rightarrow\ E(x)=0.2\times(1)+0.8(-1)=-0.6$

Hence, the  expected value of the number of points you get = -0.6