This statement is incorrect
BIRTH OF A GIRL IN MOSCOW WILL INCREASE THE CHANCE OF BIRTH OF A BOY IN NEW-YORK
Suppose again the coin experiment and flip the coin 4 times. Suppose you would get heads on your first three flips. Then the probability to get a heads on your fourth flip remains 1/2. It does not increase.
Of course the probability that you will get 2 heads over four flips is higher than 3 heads over four flips since in this statement a specific order is not assigned (for example assigning an order would be saying the first 3 flips are heads and the lasts is tails).
RE: Probability-The Mathematics that decides Life (A Brief Research Article)