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Your probability calculations are invalid.

> Lets assume for simplicity, there is only one habitable planet in the entire Milkyway galaxy, Earth. And there are 'y' number of planets in Milkyway in total.

Okay...

> Then, the probability of finding a habitable planet (Earth) in such a galaxy is 1/y.

This does not follow. I'm going to quote Feynmann here:

"You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!"




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