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An experimental protocol developed by NuGenCanPharm Inc to test if a cancer drug is effective is correct 99% of the time, on both effective and ineffective drugs. NuGenCanPharm Inc synthesizes 10,000 candidate drugs, expecting about 20 of them to actually be effective. The seventh drug they test passes the test as effective. What is the probability that, on their seventh try, NuGenCanPharm has actually found an effective cancer drug?

I was thinking that it would just be $$.99\left(\frac{20}{10000}\right)\left(1 - \frac{20}{10000}\right)^6 \approx .002 $$

however, this doesn't seem correct.

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  • $\begingroup$ It is indeed wrong. You need to consider the probabilities that (a) the seventh drug is effective and tests positive and (b) the seventh drug is not effective but tests positive. I suspect that you are expected to ignore the previous six drugs $\endgroup$ – Henry Jan 6 at 21:34

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