User blog comment:Tuner King 5/Help plz/@comment-24808864-20160112230745/@comment-24808864-20160112231309

Sorry, I try to leave short messages instead of long ones, otherwise sometimes the message is not uploaded and I have to retype.

Now, the way you are defining P(A') you have actually created a (correct) formula for "Suppose that there are n people in a room. What is the probablility that at least two people in the same room have the same birthday (ignoring birth year)."

Then your question seems to be "For what n, is the probability for event A' increasing the fastest?" (Note: not x, as you have defined the function in terms of n which is more correct anyway).