Women concerned that they have breast cancer opt to have a biopsy done. Suppose

ID: 3300361 • Letter: W

Question

that 30% of the women biopsied actually have breast cancer (the rate is high because only those

who are worried choose to do the biopsy and these women have a greater probability of having the

disease). Further suppose the test yields a false positive rate of 2% and a false negative rate of 14%.

(a)

What is the probability that a woman with a positive result has cancer?

(b)

What is the probability that a woman with a negative result has cancer?

a) The women with poisitive result:

True positive rate: TP= TP/(TP+FN)= 0.3/(0.3+0.14) = 0.68182

b) The probability that a women with Negative result has cancer:

False Positive rate: FP= FP/Negative= 0.02/0.56 = 0.0357

Positive Negative Positive 0.3 0.14 0.44 Negative 0.02 0.54 0.56 0.32 0.54 1

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