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A Lewis Carroll pillow problem: Probability of an obtuse triangle. (English)
Stat. Sci. 9, No. 2, 279-284 (1994).
On the 100th anniversary (1993) of Lewis Carroll’s Pillow problems, {\it E. Seneta} \lbrackStat. Sci. 8, No. 2, 180‒186 (1993)\rbrack presented a selection of the problems the author, Charles Dodgson, claims to have solved while in bed. The selection omits the one problem in continuous probability: ‘Three points are taken at random on an infinite plane. Find the chance of their being the vertices of an obtuse-angled triangle.’ Dodgson presented a solution that involves a clear error in conditioning. An alternative solution is suggested here. This solution seems rather natural and should be especially appealing to statisticians. The nature of the solution suggests a method for using transformation groups to give meaning to the phrase ‘at random’ in somewhat general situations.
Classification: A30 K50
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