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 Discussion: All Topics Topic: Events in what context? Related Item: http://mathforum.org/mathtools/tool/20226/

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 Subject: Events in what context? Author: rabeldin Date: Sep 3 2005
Jumping right in to define events and their probabilities leads to a superficial
understanding of both the mathematics of probability and its applications.

Events have a context. It is given by the description of an experiment in which
the event occurs.

For example, we can define the binomial experiment of tossing a coin to observe
whether heads or tails occurs. The context that this provides includes the
following: The coin is tossed just once. The two possibilities are heads or
tails with complementary probabilities.

Another experiment would be to toss the coin seven times. The events would be
the number of times heads shows, 0,1,2,3,4,5,6,7.

A third experiment would be to toss the coin until a sequence of two heads
appears and to ignore all but the last 7 throws. Here too the events would be
the number of heads, 0...7 but the context is quite different.

In summary, I recommend that discussion of "events" always be preceded by
describing the experiment, or context, of those events. Failure to do so can
lead to some common misunderstandings of probability.

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