-
When the various outcomes of an experiment are equally likely
- i.e. the same probability is assigned to each simple event,
- the task of computing probabilities reduces to counting.
-
Letting
- denote the number of outcomes in a sample space and
- represent the number of outcomes contained in an event ,
- P\left( A\right) = \frac{N\left( A\right) }{N} \tag{2.1}
-
If
- a list of the outcomes is easily obtained and
- is small,
-
then and can be determined without the benefit of any general counting principles.
-
There are, however, many experiments for which the effort involved in constructing such a list is prohibitive
- because is quite large.
-
By exploiting some general counting rules,
-
it is possible to compute probabilities of the form (2.1) without a listing of outcomes.
- These rules are also useful in many problems involving outcomes that are not equally likely.
- Several of the rules developed here will be used in studying probability distributions in the next chapter.
2.3.1 The Product Rule for Ordered Pairs
2.3.2 A More General Product Rule