6. In April 2003, Science magazine reported on a new computer-based test for ova

Question

6. In April 2003, Science magazine reported on a new computer-based test for ovarian cancer, “clinical proteomics” that examines a blood sample for the presence of certain patterns of proteins. Ovarian cancer though dangerous, is very rare, afflicting only 1 in 5000 women. The test detects the presence of ovarian cancer in 99 % of women who have the disease and 5% of women who do not have the disease.

Draw a tree diagram!!!

a) For what percentage of women does this test return a false positive?

b) For what percentage of women does this test return a false negative?

c) What is the probability that a randomly selected woman has ovarian cancer and tests positive?

d) What is the probability that a randomly selected woman does not have ovarian cancer and tests negative?

e) What percentage of women who test positive using clinical proteomics do actually have ovarian cancer?

Explanation / Answer

a)percentage of women does this test return a false positive =5%

b)percentage of women does this test return a false negative =(100-99) =1%

c) probability that a randomly selected woman has ovarian cancer and tests positive =(1/5000)*0.99=0.000198

d) probability that a randomly selected woman does not have ovarian cancer and tests negative

=(1-1/5000)*0.95=0.9481

e)probability of test positive =P( have ovarian cancer and test positive+does not have ovarian cancer and test positive) =(1/5000)*0.99+(1-1/5000)*0.05=0.050188

therefore probability of actually have ovarian cancer given test positive

=P( have ovarian cancer and test positive)/P(test positive)=(1/5000)*0.99/0.050188=0.003945

please revert for any clarification requiierd,

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