What is Probability?
With regard to health outcomes probability is the proportion or percentage of events that occur in a group of people, i.e., the number of health outcomes or "events" divided by the total number of possible events.
Probabilities can be expressed as:
 A proportion from 0 to 1, e.g., 0.32 or
 A percentage, e.g., 0.32=32%
Example:
In the Physicians' Health Study on aspirin, male physicians were randomly assigned to take an aspirin or a placebo every other day.
MI 
No MI 
Total 
Probability 

Aspirin 
126 
10,911 
11,037 
126/11,037 = 0.0114= 1.14% 
Placebo 
213 
10,821 
11,034 
213/11,034 = 0.0193= 1.93% 
Test Yourself
Consider the data in the table below from the New York City Cancer Registry
(Selected data from http://www.health.state.ny.us/statistics/cancer/registry/about.htm)
Cancer Type 
White Male 
White Female 
Black Male 
Black Female 
Total 
Colorectal 
1,236 
1,251 
449 
584 
3,520 
Liver 
330 
134 
149 
57 
670 
Lung 
1,449 
1,332 
537 
497 
3,815 
Thyroid 
175 
537 
29 
135 
876 
NonHodgkins 
582 
523 
170 
159 
1,434 
Leukemia 
348 
285 
87 
85 
805 
TOTALS 
4,120 
4,062 
1,421 
1,517 
11,120 
What is the:
 Probability that a cancer patient is a black male? [P(Black male)]
 Probability that a cancer patient has thyroid cancer? [P(thyroid cancer)]
 Probability that a cancer patient is a white female with liver cancer? [P(White female with liver cancer)]
 Probability that a cancer patient is a black with lung cancer? [P(Black patient with lung cancer)]
Work these out yourself before looking at the answers.
Conditional Probability
Conditional probability is the probability of an event occurring, given that another condition is true or another event has occurred.
Example: What proportion of patients with colorectal cancer are white?
Another way of stating this question is "Given that a patient has colorectal cancer, what is the probability that the patient is white?
The notation for this is P(white  colorectal cancer), where the "" signals the condition. In this case, P(white  colorectal cancer) = (1236 + 1251)/3520 = 0.7065 = 71%.
Test Yourself
Using the data in the table above:
 What proportion of patients with leukemia are white?
 What proportion of women have lung cancer?
Work these out yourself before looking at the answers.