So the task says: Random variable X has binomial distribution, what is the most probable realization of random variable X?
so of course it must be p0 <= p1 <= ... <= pk and pk >= pk+1 >= ... pn. So they first divede pk and pk-1 than pk and pk+1. When dividing pk and pk+1 they get this https://i.stack.imgur.com/mCKf9.jpg . That is they find that k<= (n+1) * p - 1 but i keep getting k<= (n+1) * p - n. I know they replaced q with (1-p) but I don't how did they got - 1 instead of - n, maybe my algebra is wrong but I don't know where did made a mistake.
Can someone please explain to me how did they gone from q*(n - k) >= p*(k + 1) to k >= (n+1)*p - 1 ?
Thank you!