“head” has occurred 563 times the answer would be that the probability for “head” is 0.563.
However, as the number of experiments is increased the probability would converge towards
0.5. In the mind of a frequentist, probability is a characteristic of nature.
Classical Definition
The classical probability definition originates from the days when the probability calculus
was founded by Pascal and Fermat^1. The inspiration for this theory was found in the games of
cards and dice. The classical definition of the probability of the event A can be formulated as:
() A
totPA n
n(2.2)
where:
nA = number of equally likely ways by which an experiment may lead to A
ntot = total number of equally likely ways in the experiment.According to the classical definition of probability, the probability of achieving a “head”
when flipping a coin would be 0.5 as there is only one possible way to achieve a “head” and
there are two equally likely outcomes of the experiment.
In fact there is no real contradiction to the frequentistic definition, but the following
differences may be observed:
The experiment does not need to be carried out as the answer is known in advance.
The classical theory gives no solution unless all equally possible ways can be derived
analytically.
Bayesian Definition
In the Bayesian interpretation the probability of the event is formulated as a degree
of belief that will occur:
PA() A
A
PA() = degree of belief that A will occur (2.3)Coming back to the coin-flipping problem an engineer following the Bayesian interpretation
would argue that there are two possibilities, and as she has no preferences as to “head” or
“tail” she would judge the probability of achieving a “head” to be 0.5.
(^1) Pierre de Fermat, mathematician, 1601-1665; Blaise Pascal, mathematician, 1623-1662.