Mathematics: 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?

Set up an equation 5,2000+6.5x=10,400 and solve for x...

Given the following statistics for women over the

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triciamarler

05.01.2022

Mathematics

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 ) = $\frac{P(\text{breast cancer}) \times P(\frac{positive}{\text{cancer}})}{P(\text{breast cancer}) \times P(\frac{positive}{\text{cancer}}) + P(\text{ no breast cancer}) \times P(\frac{positive}{\text{no cancer}})}$

Substitute the values :

P(breast cancer | positive ) = $\frac{0.10 \times 0.90}{0.10 \times 0.90+0.99 \times 0.08}$

P(breast cancer | positive ) = 0.531

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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