To illustrate this notion, consider the choice of whether to take an umbrella on a
cloudy, dark morning. As a simple binary matter, the outcomes can be rain or no rain.
We have two alternatives: take an umbrella or do not. The information we consider in
making this decision could be as unsophisticated as our own feelings about the weather on
similar days in the past or as sophisticated as a large-scale meteorological analysis from
the national weather service. Whatever the source of information, it will be associated
with some degree of uncertainty. Suppose we decide to take the umbrella after weighing
all the information, and it does not rain. Did we make a bad decision? Perhaps not. Eight
times out of ten in circumstances just like this one, it probably rained. This particular
occasion may have been one of the two out of ten situations when it did not.