• 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

2.3.3 Permutations and Combinations

EXERCISES Section 2.3 (29-44)