This topic mainly investigates the solution of probability and the application of distribution table and expectation.

To get 40 points, you must answer all eight multiple-choice questions correctly. Among the other four questions, the probability of answering two questions correctly is, the probability of answering one question correctly is, and the probability of answering another question correctly is, so the probability of getting 40 points is.

. ?

(2) According to the meaning of the question, the scores of candidates are 20, 25, 30, 35 and 40. 20 points means that only 4 questions are done right, and everything else is done wrong, so the probability of finding is;

Similarly, the probability of getting 25 points is

;

The probability of getting 30 points is;

The probability of getting 35 points is;

What is the probability of 40 points?

So the distribution list is

20

25

30

35

40

?

Therefore =

The mathematical expectation of candidates' scores is.