Records indicate that 2% of the population has a certain kind of cancer. a medical test has been devised to help detect this kind of cancer. if a person does have the cancer, the test will detect it 98% of the time. however, 3% of the time the test will indicate that a person has the cancer when in fact he or she does not. for persons using this test, what is the probability that the person has this type of cancer and the test indicates he or she has it? The person does not have this type of cancer, given a positive test result?
2007-05-06 15:19:12 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Probability that a person has cancer = 0.02. Probability that it is detected in that person = .98. So for a random person, the probability that he has it and that it will be detected is .98 x .02.
There is a .98 probability that he does NOT have cancer. But among that subset, 3% get detected as a false positive. hence the probability of a person not having cancer but coming up positive is .98 x .03.
The implications of this are important! It means that 3/5 of the positives are false positives! In other words, if the test tells you that you have cancer, there is only a 40% chance that that is true.
2007-05-06 15:38:21 · answer #1 · answered by Astronomer1980 3 · 1⤊ 0⤋
.02*.98 + .98*.03=.049 for a false positive
98% chance of detction if the person has this cancer.
2007-05-06 15:29:29 · answer #2 · answered by bruinfan 7 · 0⤊ 1⤋