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Probabilities of events are expressed as numbers ranging from 0 to 1, or 0% to 100%. The closer the probability of a given event is to 1, the more likely it is that the event will occur. The closer the probability of a given event is to 0, the less likely it is that the event will occur.

To compute the empirical probability of event E, denoted P(E), is:
P(E)=(observed number of times E occurs)/(total number of observed occurences)

Q. The data in the table are based on 100,000 U.S. women, ages 40 to 50, who participated in mammography screening.

Breast Cancer No Breast Cancer
Positive Mammogram 720 6944
Negative Mammogram 80 92,256

a) Find the probability that a woman aged 40 to 50 has a positive mammogram.
b) Among women with breast cancer, find the probability of a positive mammogram.
c) Among women with positive mammograms, find the probability of having breast cancer.

Source: Algebra and Trigonometry, 6e. Blitzer.

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