5. switched-conditionals Fallacy. is tested for skin cancer using a screening te

Question

5. switched-conditionals Fallacy. is tested for skin cancer using a screening test that is 95% accurate. Unfortunately, her screening test result came back positive. The doctor reminds Barbara of the screening test's 95% accuracy and tells her that that means there is a 95% chance that she has skin cancer. Fortunately, Barbara understands the Switched-Conditionals Fallacy and knows the chances are lower. What are the chances that Barbara has skin cancer, given that her test came back positive? Barbara belongs to a population in which 1% have skin cancer. Barbara

Explanation / Answer

P(positive test)=P(has skin cancer and test positive)+P(not has skin cancer and test positive)

=0.01*0.95+(1-0.01)*(1-0.95)=0.059

hence P(has skin cancer given test came back positive)=P(has skin cancer and test positive)/P(positive test)

=0.01*0.95/0.059 =0.1610

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