Unfortunately, if you wanted to find the probability of something like rain tomorrow or of a licensed driver in Louisiana being involved in an auto accident this year, the classical definition does not apply. Fortunately, there is another definition of probability to apply in these cases. Empirical Definition of Probability. The probability of event A is the number approached by.
The idea that the fraction in the previous definition will approach a certain number as the total number of recorded outcomes becomes very large is called the Law of Large Numbers.
Because of this law, when the Classical Definition applies to an event A , the probabilities found by either definition should be the same. In other words, if you keep rolling a die, the ratio of the total number of twos to the total number of rolls should approach one-sixth. In working with the empirical definition, most of the time you have to settle for an estimate of the probability involved.
This estimate is thus called an empirical estimate. Example 4 To estimate the probability of a licensed driver in Louisiana being involved in an auto accident this year, you could use the ratio. To do better than that, you could use the number of accidents for the last five years and the total number of Louisiana drivers in the last five years.
Or to do even better, use the numbers for the last ten years or, better yet, the last twenty years. Example 5 Estimating the probability of rain tomorrow would be a little more difficult. You could note today's temperature, barometric pressure, prevailing wind direction, and whether or not there are rain clouds that could be blown into your area by tomorrow. Then you could find all days on record in the past with similar temperatures, pressures, and wind directions, and clouds in the right location.
Your rainfall estimate would then be the ratio. To make your estimate better, you might want to add in humidity, wind speed, or season of the year. Or maybe if there seemed to be no relation between humidity levels and rainfall, you might want add in the days that did not meet your humidity level requirements and thus increase the total number of days.
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