This chapter will indicate how a knowledge of the theory of probability as outlined in the previous chapter can be used to make deductions as to the shape of the frequency distributions produced when certain types of experiment are repeated. The classes of experiments considered have two main characteristics in common:

1. (i) Each experiment is independent of the result of the preceding experiments. Thus the fact that a coin, when tossed, comes down heads does not affect the chance of the coin coming down heads at the succeeding tossing.

2. (ii) The quantity studied is the presence or absence of some characteristic; that is, there are only two classes to be considered and every event falls into one or other of these. These may be, for example, the heads or tails for a coin tossing experiment, under 6 ft. or over 6 ft. in height for men drawn from some population, or the presence or absence of some defect in articles made by a machine.

In the previous chapter it was found that if repeated independent drawings are made from the population under consideration, the proportion of individuals in the drawings possessing the characteristic concerned will approach the proportion in the whole population possessing it. But in all sets of drawings there will be some variation from the exact proportion, these variations depending on the size of the sets of drawings and the frequency with which the particular characteristic occurs.