3 Probability and Probability Models
3.1 PROBABILITY
Most of Chapter 1 dealt with proportions. A proportion is defined to represent
the relative size of the portion of a population with a certain (binary) charac-
teristic. For example,disease prevalenceis the proportion of a population with
a disease. Similarly, we can talk about the proportion of positive reactors to a
certain screening test, the proportion of males in colleges, and so on. A pro-
portion is used as a descriptive measure for a target population with respect to
a binary or dichotomous characteristic. It is a number between 0 and 1 (or
100%); the larger the number, the larger the subpopulation with the chacteristic
[e.g., 70% male meansmoremales (than 50%)].
Now consider a population with certain binary characteristic. Arandom
selectionis defined as one in which each person has an equalchanceof being
selected. What is thechance that a person with the characteristic will be
selected (e.g., the chance of selecting, say, a diseased person)? The answer
depends on the size of the subpopulation to which he or she belongs (i.e., the
proportion). The larger the proportion, the higher the chance (of such a person
being selected). Thatchanceis measured by the proportion, a number between
0 and 1, called theprobability.Proportionmeasures size; it is a descriptive sta-
tistic.Probabilitymeasures chance. When we are concerned about the outcome
(stilluncertainat this stage) with a random selection, a proportion (static, no
action) becomes a probability (action about to be taken). Think of this simple
example about a box containing 100 marbles, 90 of them red and the other 10
blue. If the question is: ‘‘Are there red marbles in the box?’’, someone who saw
the box’s contents would answer ‘‘90%.’’ But if the question is: ‘‘If I take one
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