If the score of the solution (1) is 50, the question 10 must be done correctly. Among the other three questions, the correct answer probability of 1 question is 1 2, 1 question is 1 3, and 1 question is 13.

So the probability of getting 50 points is: p =12? 1 3 ? 1 4 = 1 24 .

(2) According to the meaning of the question, the score range of this candidate is {35, 40, 45, 50}.

35 points means that only 7 questions are done correctly, and the rest are done wrong.

So the probability is p1=12? 2 3 ? 3 4 = 6 24 = 1 4 ,

The probability of getting 40 points is: p 2 =12? 2 3 ? 3 4 + 1 2 ? 1 3 ? 3 4 + 1 2 ? 2 3 ? 1 4 = 1 1 24 .

Similarly, the probability of getting 45 points is: p 3 = 6 24.

The probability of getting 50 points is: p 4 = 1 24.

So the distribution list with a score of ξ is:

ξ 35 40 45 50 p14124 624124 Mathematical expectation e ξ = 35×14+40×124+45× 624+.