Home About us Mathematical Epidemiology Rweb EPITools Statistics Notes Web Design Contact us Links |

> Home > Statistics Notes > Probability > Conditional Probability

But a public health epidemiologist may be interested in for instance the fraction of smokers who have coronary heart disease. In this case, he or she would use just the total number of smokers as the denominator, and the numerator would be the number of smokers with heart disease: #(SC)/(#(SC)+#(SH)). We are going to call the number of smokers #(S)=#(SC)+#(SH); it is the number of smokers with coronary heart disease plus the number without it.

So we can call the frequency of CHD among smokers f(C|S)= #(SC)/#(S); it is the number of smokers with CHD over the total number of smokers. We can also define f(S) to be the frequency of smokers f(S)=#(S)/M. Finally, let's call the relative frequency of having CHD and being a smoker f(SC)=#(SC)/M. We can now take the expression for f(C|S) and divide the numerator and the denominator both by M; this gives us f(C|S)=(#(SC)/M)/(#(S)/M), which is the same as f(C|S)=f(SC)/f(S). So we can find the frequency of CHD among the smokers just from the frequencies.

Since probabilities are meant to be long run limiting frequencies after repeating the experiment infinitely often, it made sense to define a similar concept in probability theory. Suppose that

Example. Suppose we know that the probability that a person is a smoker is 0.2 (which is 20%), and the probability that a person in our population is both a smoker and has CHD is 2%. Also suppose we happen to know that the probability that a person is both a nonsmoker and has CHD is 4%. Most of our CHD in this population is in the nonsmokers, but then again most of the people are nonsmokers. Then the conditional probability of having CHD given that a person is a smoker would be 0.02/0.2 = 0.1, or ten percent. We can also calculate the conditional probability of having CHD given that a person is a nonsmoker is 0.04/0.8=0.05.

On to independence.

Return to statistics page.

Return to probability page.

Return to stochastic seminar.

All content © 2000 Mathepi.Com (except R and Rweb).

About us.