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harlon852
30.03.2020 •
Mathematics
Suppose that, of women who undergo routine screening, 1/101 have breast cancer. Of the women who undergo screening and do have breast cancer, 80% will have a positive test. Of the women who undergo screening but don't have breast cancer, only 5% have a positive test. A woman of this age undergoes routine screening and has a positive test. What is the probability that she has breast cancer
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Ответ:
The probability that she has breast cancer if she gives a positive test result is P=0,16.
Step-by-step explanation:
The information we have is:
P(C)=1/101≈0.01
P(H)=100/101≈0.99
P(P|C)=0.80 (probability of having a positive result given that the patient has cancer)
P(P|H)=0.05 (probability of having a positive result given that the patient hasn't cancer)
where the events are:
C: have cancer
H: not have cancer
P: positive test
We need to calculate P(C|P), the probability of having cancer given a positive test result.
According to the Bayes theorem, we have:
The probability that she has breast cancer if she gives a positive test result is P=0,16.
Ответ:
x+x+2+x+4= 40+x
3x+6=40+x
2x+6=40
2x=34
x=17
Final answers: 17, 19, 21