Probability Explanation And Exercises Worksheet Page 3
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37August 1 that had the same humidity as the next occurrence of August 1. Of
course, wind direction also affects probability. You can see that our sample of prior
cases will soon be reduced to the empty set. Anyway, past meteorological history is
misleading if the climate is changing.
For some purposes, probability is best thought of as subjective. Questions
such as “What is the probability that Ms. Garcia will defeat Mr. Smith in an
upcoming congressional election?” do not conveniently fit into either the symmetry
or frequency approaches to probability. Rather, assigning probability 0.7 (say) to
this event seems to reflect the speaker's personal opinion --- perhaps his
willingness to bet according to certain odds. Such an approach to probability,
however, seems to lose the objective content of the idea of chance; probability
becomes mere opinion.
Two people might attach different probabilities to the election outcome, yet
there would be no criterion for calling one “right” and the other “wrong.” We
cannot call one of the two people right simply because she assigned higher
probability to the outcome that actually transpires. After all, you would be right to
attribute probability 1/6 to throwing a six with a fair die, and your friend who
attributes 2/3 to this event would be wrong. And you are still right (and your friend
is still wrong) even if the die ends up showing a six! The lack of objective criteria
for adjudicating claims about probabilities in the subjective perspective is an
unattractive feature of it for many scholars.
Like most work in the field, the present text adopts the frequentist approach
to probability in most cases. Moreover, almost all the probabilities we shall
encounter will be nondogmatic, that is, neither zero nor one. An event with
probability 0 has no chance of occurring; an event of probability 1 is certain to
occur. It is hard to think of any examples of interest to statistics in which the
probability is either 0 or 1. (Even the probability that the Sun will come up
tomorrow is less than 1.)
The following example illustrates our attitude about probabilities. Suppose
you wish to know what the weather will be like next Saturday because you are
planning a picnic. You turn on your radio, and the weather person says, “There is a
10% chance of rain.” You decide to have the picnic outdoors and, lo and behold, it
rains. You are furious with the weather person. But was she wrong? No, she did not
say it would not rain, only that rain was unlikely. She would have been flatly
wrong only if she said that the probability is 0 and it subsequently rained.
187
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