freak results, for example turning up the same card on ten consecutive
occasions, do not greatly distort the figures because of the large number of
occasions on which a card has been drawn. To illustrate, assume after 52
million draws the Ace of Hearts is then drawn ten times. This will have
negligible impact on the relative frequency, that is the number of occasions
when the queen of hearts has been drawn compared to other cards because 10
is such a small number compared to 1 million.
How Often Predicting How Likely
Probability of “how often” is a predictor of “how likely”. Assume that the
medical data for the occurrence of a disease (“how often”) is that 56% of
people who have done X, for example reached age 70, have contracted
disease Y. Jack is now 70. What does the data say about the likelihood that
Jack has disease Y? If we have no better information on “how likely” than
“how often,” our best guess is to use “how often” all the time. In the long run,
that is if we do this consistently and over a reasonable number of trials, we
minimise the extent of errors in our prediction more than if we had consistently
used some other measure. Thus, in the absence of additional information, our
best guess is that Jack’s chance of having disease Y is 56%.
Assigning Probability
Introduction
Aside from any outstanding philosophical issues with the foundations of
probability, there is an issue with how an initial probability is assigned to the
happening of an event or to the truth of (that is, the validity and reliability of) a
causal law. Our concern with the probability of the happening of an event
arises because that is the task a court has to do when it find facts. Our
concern with the probability that causal or behavioural law is true arises
because a legislature enacting a statute or a court interpreting a statute or
common law rule needs to know this type of probability in order to perform its
task,
Happening of an Event
Several means are proposed for determining the probability that some event
will happen. These are single observation, systematic observation and
symmetrical evidence.
Single Observation
Individual
In the real world we all live our live on this basis that
when we observe
something we know that what we have observed. As the saying goes, seeing is
believing. This is why one reason that a person may believe that they know
something is that they have observed it. They can observe it with any of their
five senses, namely sight, sound, touch, taste and hearing.
 |
 |
 |