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A doctor thinks that, when treated with a new drug, a patient has a probability of $\frac25$ to improve. How many patients must he treat to be sure (at $p >.95$) that at least one patient will improve?

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What have you tried? Any thoughts on what distribution is appropriate? Are the patient results independent? –  Ross Millikan Nov 9 '12 at 5:23

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up vote 0 down vote accepted

Hints:

  • If the probability a patient will improve is $p$ then the probability a patient will not improve is $q=1-p$

  • If the patients' improvements are independent then the probability none of $n$ of them will improve is $q^n$

  • What probability values do you want for this event?

Set up the inequality and solve, possibly using logarithms and rounding.

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