Need to figure out a formula for calculating sample size


New Member
One of the regulations that I am required to use in my profession asks to demonstrate that the selected sample size is adequate. Attached is an example that they have given and I need help figure out the formula on how they calculated the "Number of subjects studies (n)"

"A reasonable probability (80%) of observing at least one event of an undesirable side-effect when 15 subjects are studied requires a side-effect with an actual probability of 10%. If only 15 patients have been studied, from a statistical point of view, there could be serious side-effects with an actual probability of 10% that have not had a reasonable chance to be detected. The device would only be acceptable (for any type and severity of undesirable side-effects), if that magnitude is
acceptable when weighted against the performance of the device and the current state of the art.
The attachment shows corresponding numbers for undesirable side-effects with an actual probability of 10%, 5% and 1%."