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Colorectal cancer has a base rate of 4%. A fecal occult blood test used to detect colorectal cancer has sensitivity 77% and specificity 57%. Among those who tested negative, roughly what percentage has colorectal cancer? A) 2% B) 3% C) 4% D) 5%

I calculated P(NEG)= P(NEG and CANCER) + P(NEG and NO CANCER) = 4*23/10000 + 96*57/10000. Then I took P(NEG and CANCER)/ P(NEG)

The final answer I got was 0.0165, so rounded up it would be option A. Am I doing this correctly?

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    I am not overly familiar with the terms "sensitivity" and "specificity" in this context, but I assume the refer to the conditional probabilities of getting a correct result given that the patient actually has colorectal cancer / doesn't have colorectal cancer. Which one is which? – 2017-02-15
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    @Arthur Yes you are quite right. Sensitivity is P(POS|Cancer) and specificity is P(NEG|No cancer). – 2017-02-15
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    Looks good to me. – 2017-02-15

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