Probabilities for a finite population

Random sampling from populations is described using probability. If one value is sampled from a finite population of N distinct values, we say that

Many populations contain values that occur more than once. When sampling from any population,

The probability that a single sampled value is either x, y, ... is the proportion of population values that are either x, y, ... .

For numerical populations, the most useful form of this result is:

Prob( a < X < b )   =   propn of values between a and b.