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Approaches to probability 73
Approaches to probability
There are three different approaches to deriving probabilities: the
classical approach, the relative frequency approach and the subjective
approach. The first two methods lead to what are often referred to
as objective probabilities because, if they have access to the same information,
different people using either of these approaches should arrive
at exactly the same probabilities. In contrast, if the subjective approach
is adopted it is likely that people will differ in the probabilities which
they put forward.
The classical approach
Consider the following problem. You work for a company which is a
rather dubious supplier of electronic components and you have just
sent a batch of 200 components to a customer. You know that 80 of the
components are damaged beyond repair, 30 are slightly damaged and
the rest are in working order. Moreover, you know that before he signs
the acceptance form the customer always picks out one component at
random and tests it. What are the chances that the customer will select a
component which is damaged beyond repair?
The classical approach to probability involves the application of the
following formula:
The probability of an event occurring
= Number of outcomes which represent the occurrence of the event
Total number of possible outcomes
In our problem the customer could select any one of the 200 components,
so there are 200 possible outcomes. In 80 of these outcomes a component
is selected which is damaged beyond repair so:
p(selected component is damaged beyond repair) = 80/200 = 0.40
In order to apply the classical approach to a problem we have to
assume that each outcome is equally likely to occur, so in this case we
would have to assume that the customer is equally likely to select each
component. Of course, this would not be the case if you knew that the
customer tended to select a component from the top of the box and you
deliberately packed the defective components in the bottom. In most