This problem was on my Probability final a month ago... and to this day, I still haven't figured it out yet. Here it is:
A theater has a set of seats consisting of four rows and twelve columns for a total of 48 seats. 10 people walk into the theater and each person takes a seat at random. Let X be the number of people with someone sitting directly in front of them. What is the expected value of X? Note: In the following case, Sally is sitting directly in front of Mike: Empty Seat Sally Mike In the following case, Fred is NOT sitting directly in front of George: Fred Empty Seat George . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
