MGSC 1206 May-June, 2016 Due 02 June, 5pm (130 points) Assignment 3 1. Use shading to show each set in the Venn diagram. A A B B ?? ?? (A?B)?B (a) A?B (4 points) (b) (4 points) 2. Suppose that P(A?B)=0.8, P(A)=0.5P(B'). Determine P(A). (10 points) (1) Assume that A and B are independent (2)Assume that A and B are mutually exclusive. 3. We usually design two versions of the midterm exam paper for the course MGSC 1206. We do not have the cameras in the classrooms. In May, 2016, Version A had the same statements as Version B except for one number in each of Question 1, 2, and 3. (For example, Question 2 of Assignment 3, one version is with P(A)=0.5P(B'), and the other version is with P(A)=2P(B').) John worked on Version A, but the solutions are with the same numbers of Version B. Moreover, John made mistakes in the solving processes of these three questions. As a result, John could have got only several points even if the number differences had been ignored. As we know well, it is possible for a person to make mistakes on reading. According to history data, a person has such a mistake in one question with the probability 5%. Suppose that a person makes the mistake in different questions are independent. (1) What is the probability that John did the exam by himself according to the history data? (2 points) (2) The instructor doubts that John was cheating in the exam. What is the best solution for the instructor? Explain. (20 points) (3) Suppose that the instructor claimed that John cheated. According to the management policy, the cheating behaviour will be recorded into John’s file. John had a chance to talk with the instructor before the instructor reported it to the university. In the meeting, John said that he got a lot of difficulties in life, and had not got much benefit from the behaviour. John negotiated with the instructor,...
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