symmetrical, the outcome would more likely be 0.5 (ratio of 1/2) 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 cer-
tain 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 com-
panies get around this by using a much larger population sample and constantly revis-
ing the figures as new data are obtained. Thus, even though many people question the
validity of such “broadbrush” results, the insurance companies believe that, probabili-
ty-wise, the values they use are valid for most large groups of people and under most
conditions of life.
How are probabilities of compound eventsdetermined?
Besides the probability of simple events, probabilities of compound events can also be
computed. For example, if xand yrepresent two independent events, the probability 247
APPLIED MATHEMATICS
What is subjective probability?
A
s the word implies, a subjective probability is thought of as a personal
degree of belief that a particular event will occur. An individual’s personal
judgment is not based on any precise computation, but is most often a reason-
able assessment of what will happen by a knowledgeable person. This is usually
expressed on a scale of 1 to 0, or on the percentage scale. For example, if a per-
son’s baseball team has a winning streak, they might believe that their team has
a probability of 0.9 of winning the division championship for the year. More like-
ly, they will say their team has a 90 percent chance of winning, not because of
any mathematical formula, but only because the team has had a winning record
during the year.