Checkpoint 4.9.4. Mean Tough Teacher.

You are in a probability and statistics class with a teacher who has predetermined that only one student can make an A for the course. To be "fair", he places a number of slips of paper in a bowl equal to the number of students in the course with one of the slips having an A designation. Students in the course each can pick once randomly from the bowl and without replacement to see if they can get the lucky slip. Determine the following:
  1. If there are 15 students in your course, determine the probabilities of getting an A in the course if you pick first and if you pick last.
  2. Since the teacher likes you the most, she will give you the option of deciding whether to pick at any position. If so, determine the position that would give you the best likelihood of getting the A slop.
  3. Suppose again that the teacher was feeling more generous and decided instead to allow for two A’s. Determine how that changes your likelihood of winning and on what position you would like to choose.
  4. Continue as above except that only one slip does not have an A on it.
  5. Discuss how your choice is affected by the number of students in the course or the number of A slips included.
Solution.
in-context