Not quite. What you calculated is the probability that visitors will not hit the p99 case on all their requests. In other words, the chance of getting a p99 response on all 100 requests is infinitesimal.
The chance of getting at least one p99 response out of a hundred is 1 - 0.99^100 ≈ 63%.
https://latencytipoftheday.blogspot.com/2014/06/latencytipof...