MATH STINGER #39
by Dr. Joel C. Fowler
Assistant Professor of Mathematics

The last puzzle of the summer involved probability. Suppose that 6 people are seated in a row at a theater next to each other. There is an aisle at either end of the row. At the end of the movie they leave at random one by one. Thus it is possible that a person leaving may have to step over some of those that remain in order to reach the aisle. Find the probability that sometime during the entire exodus at least one person will have to step over another to get out. Only the order that they leave in is random. The direction that they leave in is determined by whether they must step over another person. In other words, if the next person to leave is on either end of those that remain, then they will not step over anyone. If they aren't, then they must step over someone. This puzzle was solved correctly by several people, but at the request of Professor Flannery I will issue it as a challenge to all Math 260 (Probability and Statistics) students and delay the answer until next issue. After you have solved the puzzle in its original form you may wish to find a general formula for the probability when n people are in the row. Another variation that is more difficult is to determine the probability that at least one person will be stepped over when 8 people are seated in two groups of 4. That is, there is an aisle down the center of the group, as well as at each end.

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