Binomial Probability to find N? Problem

Question

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?

Answer 1

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.