Question

Mammograms are a relatively inexpensive and nonintrusive way to test for breast cancer. Suppose that mammogram...

Mammograms are a relatively inexpensive and nonintrusive way to test for breast cancer. Suppose that mammogram screenings are 93% specific and 87% sensitive. This means that those without breast cancer test negative 93% of the time and those with breast cancer test positive 87% of the time. Answer the following questions as if 12.6% of all women have breast cancer.

a) Given that a women tests negative, what is the probability that she has breast cancer?

(b) Given that a women tests positive, what is the probability that she does not have breast cancer?

(c) In your opinion, are mammograms effective diagnostic tools? Please explain your answer.

Math   Statistics-And-Probability   
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Answer #1

a)

P(tested negative)=P(have cancer and tested negative)+P(not have cancer and tested negative)
=0.126*(1-0.87)+(1-0.126)*0.93=0.8292
Therefore P(have cancer|tested negative)=0.126*0.13/0.8292=0.0198

b)

P(tested positive)=P(have cancer and tested positive)+P(not have cancer and tested positive)
=0.126*0.87+(1-0.126)*(1-0.93)=0.1708
Therefore P(not have cancer|tested positive)=(1-0.126)*(1-0.93)/0.1708=0.3582

c)

Since even if test comes positive ,probability of not having cancer is higher, mammograms does not appear to be effective diagnostic tools.

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