Xpectation Mania #4

In a weird alien empire, the efficiency of the community is considered to be the highest when the number of friendless individuals maximizes.

And these aliens are extremely hostile creatures. If you consider a random pair of aliens, the probability that they are friends of each other is exactly $0.1\%$ . Now, as a ruler of the alien society, you want to maximize the efficiency of the community. The variable that you are allowed to control is the total population $P$ .

So, if the number of individuals who have exactly $0$ friend is $N$ , you want to maximize $E(N)$ , which means the expected value of $N$ . Determine the value of $P$ for which $E(N)$ is maximized.