100 people study is also not terribly likely though at 73%. It gets worse - someone’s brain being eaten could be an aberration and you may have to ignore the single outlier, and your detection chances are dropping below 50%
We're finding the chance that the study will demonstrate brain eating. The hypothesis is that brain eating is rare: .01 chance of that. So any particular subject will probably not display brain eating: .99 chance of that. Assuming brain eating tests are independent, you can raise that quantity to the hundredth power to get the chance that all 100 subjects will not display brain eating. That would be a failure of the test, so subtract that chance from unity to get the test's chance of success.
My math: If there is a 1% chance of something happening in a given sample, there is a 99% chance of it not happening. So, for a set of N samples, you multiply 0.99 * 0.99 * 0.99... N times or 0.99^N to determine the chances of it not happening in any of the samples. 0.99^100 is about 0.37. 1- 0.37 = 0.63.