past data to assign probabilities in the present or future –
the process of
extrapolation – is not fully scientific, but it is generally the best basis available.
Symmetrical Evidence
If observation is possible we can observe something and therefore know that it
is true. Sometimes, however, proper observation is not possible. This happens
in the case of shuffling a deck of 52 playing cards and drawing one card from
the pack when the cards are face down. If a person could observe what
happened to every card as it was shuffled into the pack and the pack cut, and
if they could see which card, for example the 14th, was being drawn, they
could tell you for sure what card it was.
This, however, is not the case so there is uncertainty about our observation.
We have seen the cards shuffled, but we do not fully know what has happened
to each card in the process.
How do we handle this uncertainty? The key to it is that there are many ways
in which the cards can be shuffled, cut and drawn. Since an ordinary human
(as distinct from a card sharp) cannot control the ways in which they shuffle,
cut and draw a deck of cards and since there are no special factors involved
which favour one way of doing these tasks over another, there is a reasonable
assumption that each way is equally likely. Put another way, evidence for the
probability of each event or possible outcome is symmetrically balanced so
that each outcome is equally likely. Thus, the probability of drawing any
particular card from a deck of 52 is one in 52, ie 1/52.
This form of probability was the first
to excite curiosity, which it did in the
seventeenth century. Aristocratic speculation about games of chance such as
cards was the initial motivating force. This led to more serious considerations
and much of the early work was done by correspondence between two major
mathematicians, Blaise Pascal (1623-1662) and Pierre de Fermat (1601-1665).
(This correspondence, by the way, started in 1654 when Pascal was a mere 16
years of age.)
This version of probability is variously called a priori
probability, classical
probability or the frequentist view. It is used in “cases where there are a finite
number of possible outcomes each of which is assumed to be equally
probable”.
236
Gambling with cards and dice which prompted initial interest in probability
furnishes also furnishes excellent illustrations. With a deck of 52 cards, the
probability of drawing a specific card, for example the Queen of Hearts is
___________________
236
Robertson and Vianaux (1993) p 459
 |
 |
 |