JSM 2004 - Toronto

Abstract #302082

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Activity Number: 443
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Education
Abstract - #302082
Title: Some Variations of the Hat Problem
Author(s): Marepalli B. Rao*+ and Rupa Mitra
Companies: University of Cincinnati and Minnesota State University at Moorhead
Address: Center for Genome Information, Cincinnati, OH, 45267-0056,
Keywords: probability ; optimization ; strategy
Abstract:

The Hat Problem has been circulating among mathematics and statistics departments all over the world for quite some time. This is a fascinating probability problem which can be posed in any introductory probability class. The problem can be stated as follows. Belinda, Miranda, and Yolanda step on to a stage in order to win a million dollar prize collectively. Each of the members of the team is fitted by the host with a hat, which is either black or white. Each member can see the color of the hats of the other members but not her own. Each member is queried by the host separately to guess the color of her own hat. The response could be black, white, or pass. The team will get a million dollars prize provided at least one guesses the color of the hat and guesses right. The participants could get into a huddle before coming on to the stage, formulate a stragegy of responses, and then execute the strategy on the stage. The puzzle is to find a strategy which maximizes the probability of winning the prize. In this presentation, we discuss some variations of this problem.

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