We've all experienced a highly improbable event in our lives. Probably many, in fact. Some of us more than others, some more seemingly improbable than others. There is such a thing as the Law of Large Numbers that explains these coincidences and "miracles".
The Law of Large Numbers simply stated (sans math): with a large enough sample many odd coincidences are likely to happen.
Coincidence: an occasion when two or more similar things happen at the same time, especially in a way that is unlikely and surprising.
Miracle: an unusual and mysterious event that is thought to have been caused by a god, or any very surprising and unexpected event.
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On a side note, I was disappointed with Dictionary.com's listing on these words so I thought I'd go to the Cambridge Dictionary. The definition above is from the Dictionary of British English. Out of curiosity, I looked up the word miracle in the Cambridge Dictionary of American English:
Miracle: an unusual and mysterious event that is thought to have been caused by God, or any surprising and unexpected event.
A very subtle but telling difference! I think I'll be using the British version from now on.