Problem of the Week

Thanks go to Michael Lang for this week's problem. 

Because of the upcoming Thanksgiving break and the soon-to-follow end of the semester, this week's problem will be the last for the semester.  Enjoy the holidays and please visit us again after the start of the spring semester.

An airplane has exactly 80 passenger seats. Eighty passengers are in a single line to get on board, and each has a reserved assigned seat. Each passenger gets on one at a time to select his or her seat. However, the first passenger does not look at the assigned seat number and randomly selects a seat on the plane. Thereafter, each passenger takes his or her assigned seat - if it is already taken, the passenger selects  another unoccupied seat at random. What is the probability that the last passenger on board will be able to sit in his/her originally assigned seat?

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ã2003 Alberto L. Delgado