Dubinse wrote:
>
> I had promised a colleague a story that illustrates probability and
> now I forgot how to solve it formally. The story is about six
> students who go off on a trip and get drunk the weekend before
> their statistics final. They return a few days late and beg for a
> second chance to take the final exam. They tell a story about how
> they were caught in a storm and their car blew a tire and ended up
> in a ditch and they needed brief hospitalization etc. The instructor
> seems very easy going about the whole thing and tells them to report
> the next day for an exam with only one question. If they all get it right
> they all pass. They were seated at corners of the room and could not
> communicate. The one question was, "Which tire?" I remember that
> the liklihood of all four pickng the same tire was quite small, but I
> forgot how to calculate it explicitly (except for listing all the possible
> outcomes).
Pick one student (call her Alice). By symmetry it doesn't matter which
tire she picks. Then they pass if Betty, Charlene, and Dianne each
independently pick that tire, which each has 1 chance in 4 of doing; so
the answer is 1 in 4x4x4 = 64.
(On the other hand if they are in political science or international
relations and have read Schelling on "The Strategy of Conflict", they
will probably all pick the left front tire (or right front in Britain),
as the most "distinct" one. In fact, experiments have shown that this
sort of spontaneous agreement *does* occur even without special
training!)
-Robert Dawson
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