Applied Mathematics

Probability Theory

What are some simple probability events?

The probability measure of an event is sometimes defined as the ratios between the number of outcomes. There are many simple illustrations of probability events, many of which we are all familiar with. One of the simplest examples of probability is tossing a coin, with a sample space of two outcomes: heads or tails. If a coin were completely symmetrical, the outcome would more likely be 0.5 (ratio of ½) for heads and 0.5 for tails. As we all know, it never comes out that way, which may or may not mean our coins are not in perfect balance.

Another example is weather records. Many of us keep track of weather over the years. But if one were to gather all the records for the day of May 10 over 30 years from the weather service, one could do some simple probability event measurements. For example, take a (fictitious) sampling of the cloud-covered days in a certain area for the last 30 years on May 10. Say there were 10 cloud-covered May 10s in 30 years; thus, the probability measure would be a ratio of 10/30 to the event that the day will be cloudy on May 10.

Insurance tables are also figured out in a similar way. For example, if, out of a certain group of 1,000 persons who were 25 years old in 1900, 150 of them lived to be 65, then the ratio 150/1,000 is assigned as the probability that a 25-year-old person will live to be 65. On the other hand, the probability of such a person not living to be 65 is 850/1,000 (because the sum of the two measures must be equal to 1). It is true that such a probability statement is valid only for a set group of people, but insurance companies get around this by using a much larger population sample and constantly revising the figures as new data are obtained. Thus, even though many people question the validity of such “broadbrush” results, the insurance companies believe that, probability-wise, the values they use are valid for most large groups of people and under most conditions of life.


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