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Yesterday, 22:53

1% of women at age 40 who participate in routine screening have breast cancer. 80% of women with breast cancer get positive mammographies. 9.6% of women without breast cancer get positive mammographies. A 40-year old woman participates in routine screening and has a positive mammography. What's the probability she has cancer?

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  1. Yesterday, 23:20
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    0.0776

    Step-by-step explanation:

    In order to solve this problema, Baye's rule is used. Ii is expressed as follows:

    P (A if B) = (P (B if A) * P (A)) / (P (B))

    Let A be women who have cancer and let B be women who have positive mammographies

    So, P (B if A) would be women with breast cancer get positive mammographies

    P (B if A) = 0.8

    P (A) would be women with breast cancer

    P (A) = 0.01

    P (B) would be the women with positive mammographies. We don't know it.

    In order to find it we use law of total probability

    P (B) = P (positive mammographies and cancer) + P (positive mammographies without cancer)

    P (B) = 0.8*.01+0.096*0.99

    P (B) = 0.103

    With P (B) calculated we can complete the equation:

    P (A if B) = (0.8*0.01) / 0.103=0.0776

    Probability is 0.0776
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