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You are given the following statistics about 40-50 year-old women who are asymptomatic and undergo routine breast cancer screenings:

- The probability that one of these women has breast cancer is 0.008 (or 0.8%)
- If a woman has breast cancer, there is a 90% chance that the screening (diagnostic mammogram) has a positive reading — suggesting the patient does have breast cancer.
- If a woman does not have breast cancer, there is 7% chance that the screening (diagnostic mammogram) has a positive reading — suggesting the patient does have breast cancer.
Suppose you are asked to interpret a patient's mammogram screening and then provide the patient with a percentage/probability describing the likelihood that cancer is present. You read the patient's mammogram screening to see it came back positive (the woman tested positive,suggestingbreast cancer is present).

Given the positive mammogram result and the statistics described above, what is the percent chance that this particular woman actually has breast cancer?"

Sagot :

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