We have $n$ people: $\alpha n$ are boys and $(1-\alpha)n$ are girls. They are standing in a line in a random order. We pick up one boy also at random.
What can one say about the probability that there are more girls than boys before this randomly selected boy if $n\to \infty$?
Is it true that this probability is $O(1/n)$?
Yes, i meant $\alpha>0.5$. What is the correct approach to find the coefficient before $1/n$?