Downloadable - About University

Marginal and conditional probabilities 79
For example, if the probability of a project being completed on time is
0.6, what is the probability that it will not be completed on time? The
answer is easily found:
p(not completed on time) = 1 − p(completed on time)
= 1 − 0.6 = 0.4
Marginal and conditional probabilities
Consider Table 4.2, which shows the results of a survey of 1000 workers
who were employed in a branch of the chemicals industry. The workers
have been classified on the basis of whether or not they were exposed
in the past to a hazardous chemical and whether or not they have
subsequently contracted cancer.
Suppose that we want to determine the probability that a worker in
this industry will contract cancer irrespective of whether or not he or she
was exposed to the chemical. Assuming that the survey is representative
and using the relative frequency approach, we have:
p(worker contracts cancer) = 268/1000 = 0.268
This probability is called an unconditional or marginal probability
because it is not conditional on whether or not the worker was exposed
to the chemical (note that it is calculated by taking the number of workers
in the margin of the table).
Suppose that now we wish to calculate the probability of a worker
suffering from cancer given that he or she was exposed to the chemical.
The required probability is known as a conditional probability because the
probability we are calculating is conditional on the fact that the worker
has been exposed to the chemical. The probability of event A occurring
Table 4.2 – Results of a survey of workers in a branch of the chemicals industry
Contracted
cancer
Number of workers
Have not
contracted cancer Total
Exposed to chemical 220 135 355
Not exposed to chemical 48 597 645
Total 268 732 1000