A student is taking a 3 question multiple choice test. Each question has 4 options. If all the students completely guessed on every question which graph below shows the theoretical distribution of grades?

Second graph.

Step-by-step explanation:

We have 3 questions, and each question has 4 options.

Then, the probability to having one question correct by selecting an option at random is 1/3 = 0.25.

Now, the probability of answering incorrectly the question is 1 - 0.25 = 0.75

Now let's analyze the options:

Having the 3 questions wrong.

Here we have 3 times the probability of 0.75, then the joint probability is:

P = 0.75*0.75*0.75 = 0.42

Whit this we can discard the third graph, now let's calculate the probability of having one answer correct.

The probabilities are two times 0.75 and one times 0.25, but in this case, we have 3 possible combinations ( the correct one is the first, the correct one is the second, the correct one is the third) so we need to also add a factor of 3.

P = 0.75*0.75*0.25*3 = 0.42

Whit only these two calculations we can see that the correct graph is the second graph.  

We could also calculate the probabilities of having 2 correct answers (again, here we have 3 permutations, this time for the incorrect answer):

P = 0.25*0.25*0.75*3 = 0.14

The probability of having 3 correct answers is:

P = 0.25*0.25*0.25 = 0.02

(3x-8) or (3x+8)

step-by-step explanation: