a) What is wrong with the following line of reasoning?
"I was born on 18th December, that makes me quite special since the odds of a person being born on 18th December is 1 in 365"
"The population of the world is 6.7 billion. Now, the odds of each person being born on their respective birthdays becomes (1/365)^(6.7E9). Extend this to every human being, or every creature that has ever existed and the number becomes small enough to be considered impossible in practical terms"
I am certain that the above arguments are wrong and it is meaningless to talk about probability once an event has occurred, but I'm looking for a more precise mathematical answer that pin-points the fallacy in this kind of reasoning.
b) Do the following arguments fall in the same category?
i) The 'fine-tuning of the universe' argument for the existence of God
ii) The impossibility of formation of first cell against evolution