2005 STN.indd

One of the classic problems in probability theory is the “matching problem,” which is often presented as: A group of men at a party throw their hats into the middle of a room, and at the end of the party each man selects a hat at random before they leave. What is the probability that everyone gets the right hat, or that nobody does, or that at least one person does, and what is the average number of men who get their own hat? But we have found that our college students do not get excited by the context of men selecting random hats, so we often change the scenario to a more interesting one. One possibility, which is all in jest, and we apologize for the offensiveness if one takes the context seriously, is to ask students to consider a hospital staff that returns newborn babies to their mothers at random (Workshop Statistics, Activity 14-1). We use this problem and context to ask students to explore and discover fundamental ideas of probability and randomness. For younger students, the context could easily be changed to something less offensive but still likely to interest them, perhaps a group of students who throw their identical backpacks into a pile before they walk into the cafeteria and then select a backpack at random after lunch.