Terrance Fuentes

Mathematics

9 November, 17:23

A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i. e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i. e. incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i. e. negative) result, what is the probability that she has the disease?