Given the following statistics for women over the age of 50 entering our medical clinic:
(a) 1% actually have breast cancer
(b) 90% of the women who have breast cancer are going to get a positive test result (affirming that they have the disease)
(c) 8% of those that actually don’t have the disease are going to be told that they do have breast cancer (a "false positive")

what’s the actual probability, if a woman gets a positive test result, that she actually does have breast cancer?

P(breast cancer) = 0.01

P(no breast cancer ) = 1-0.01 = 0.99

P(positive | breast cancer)= 0.90

P(positive | no breast cancer ) = 0.08

P(breast cancer | positive ) =

Substitute the values :

P(breast cancer | positive ) =

P(breast cancer | positive ) =

Hence the actual probability, if a woman gets a positive test result, that she actually does have breast cancer is 0.531

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step-by-step explanation:

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