The probability of answering a question correctly is 1.3 and the probability of answering a question correctly is 1.4.
The probability of getting 40 points is P= 1 2? 1 3 ? 1 4 = 1 24
(2) According to the meaning of the question, the range of candidates' scores is 25, 30, 35 and 40.
I got 25 points in the exam, got 5 questions right, and all the other 3 questions were wrong.
The probability is p1=12? 2 3 ? 3 4 = 1 4
Getting 30 points means doing 5 questions correctly, and the remaining 3 questions are only done correctly 1 questions.
The probability is P 2 = 1 2? 2 3 ? 3 4 + 1 2 ? 1 3 ? 3 4 + 1 2 ? 2 3 ? 1 4 = 1 1 24
Getting 35 points means doing 5 questions correctly, and the remaining 3 questions mean doing 2 questions correctly.
The probability is P 3 = 1 2? 1 3 ? 3 4 + 1 2 ? 2 3 ? 1 4 + 1 2 ? 1 3 ? 1 4 = 1 4
Getting 40 points means getting 8 questions right.
The probability is P 4 = 1 24.
30 points is the most likely.
(3) The allocation list from (2) is:
ξ25 30 35 40 p 1 4 1 1 24 1 4 1 24∴eξ= 25？ 1 4 +30? 1 1 24 +35? 1 4 +40? 1 24 = 730 24 =30 5 12