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Probability and Independence

Age effects in medical care. The type of medical care a patient receives may vary with the age of the patient. A large study of women who had a breast lump investigated whether or not each woman received a mammogram and a biopsy when the lump was discovered. Here are some probabilities estimated by the study. The entries in the table are the probabilities that both of two events occur; for example, 0.321 is the probability that a patient is under 65 years of age and the tests were done. The four probabilities in the table have sum 1 because the table lists all possible outcomes.

Tests Done?
Yes No
Age under 65 0.321 0.124
Age 65 or over 0.365 0.190

(1) What is the probability that a patient in this study is under 65? That a patient is 65 or over?
(2) What is the probability that the tests were done for a patient? That they were not done?
(3) Are the events A = (the patient was 65 or older) and B = (the tests were done) independent? Were the tests omitted on older patients more or less frequently than would be the case if testing were independent of age?

Solution Summary

The solution provides step by step method for the calculation of probabilities and checking independence. Formula for the calculation and Interpretations of the results are also included.