(2) Your professor invites you to join an upcoming lecture by a faculty member visiting from Lehigh. Both faculty and students are invited to attend the lecture. Let X represent the difference between the number of faculty members and the number of students attending. a. There are n attendees. What are the possible values of X? b. Suppose n = 31. Calculate P (X = 0) Now assume there is an equal number of faculty and students at the lecture. The department chair is hosting a dinner afterwards and decides to invite 6 attendees, selected by random draw. c. What are the possible values of X? d. Calculate the probabilities for each value of X (3) In question (2) the department chair invites 6 people to dinner. Assume that there are 50 attendees at the lecture, 30 of whom are faculty members and the rest are students. Let Z represent the number of students invited to dinner a. What are the possible values of Z? b. Determine the probability mass function of Z

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A: we have probability of P(A)= 0.3 and P(B)=0.3 and P(A and B)=0.2

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A: We know that, mutually exclusive events are  events which can not happen at the same time.

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A:

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A: Given that  p(A)=0.7 , p(B)=0.2

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