I'm currently preparing for my test and I have stumbled upon a question which I am not sure how to solve. The question is as follows:
A test consists of 40 multiple choice questions to each of five possible answers given,only one of which is the correct answer. The student is asked to select the correct answer to each question. The first twenty questions (Section A) earn two marks each for the correct answer and the remaining twenty questions (Section B) earn three marks each for the correct answer. These two sections of the test are based on different and unrelated course material. All wrong answers earn zero marks (there is no negative marking). Consider a student who has not studied for the test and who answers each question by guessing.
(a) Find the probability that the student obtains exactly 70% of the marks in each of the the two sections.
This looks like a Binomial Distribution to me with n=40, p=0.2 and q=0.8. My working is to find that Pr(x=0.7). I tried that and the answer was wrong. Can anyone please explain to my why this working resulted in the wrong answer?
Thanks