Nice article Ali!

I would like to say, as I understand the probability is a ratio of all possible outcomes in your favour to the total possible outcomes.So even if the possiblity of getting a head on a coin tiss is 50 % It is quite possible that you get a head first 1000000 times and tail the next 200000 times. So the birthday paradox doesn't appear much of a paradox to me because anyways probability is no garauntee of anything unless it is one.

Hope I made sense!