Hello,
I have a question regarding the definition of probability. If I
understand correctly, probability may be defined using just axioms. However,
my textbook also uses a relative frequency definition, in which a
probability is defined as being the proportion of times an outcome occurs in
repeated trials of an experiment. This makes sense when one flip of the coin
is one trial, and in repeated trials, the proportion of heads is 1/2. But
what about a situation (an ex. in my textbook) where the probability of rain
tomorrow is 0.70. How do you define this experiment? Perhaps you measure
rainfall, temperature, pressure, etc. for each day over a long time period.
Then the probability of rain tomorrow is the proportion of times that rain
occurred on days with similar values for temp., humidity, etc.? This seems a
bit awkard to me. Also, how many trials must one perform an experiment,
before you know that the proportion converges to a particular fraction? Any
help on interpretation of relative frequency probabilities would be greatly
appreciated. In many cases, it seems difficult, at least for textbook
examples, to define what the actual experiment is.
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