You are not really interested. If you are, then you would have found the info for yourself but the following are some references :. (I also added info about the Authors)
---Rees, Martin (May 3, 2001). Just Six Numbers: The Deep Forces That Shape The Universe. New York, NY: Basic Books; First American Edition edition.
https://en.wikipedia.org/wiki/Martin_Rees
---Davis, Paul (2007). Cosmic Jackpot: Why Our Universe Is Just Right for Life. New York, NY: Orion Publications. p. 2.
ISBN 0618592261.
https://en.wikipedia.org/wiki/Paul_Davies
---Stephen Hawking, 1988. A Brief History of Time, Bantam Books,
ISBN 0-553-05340-X,
https://en.wikipedia.org/wiki/Stephen_Hawking
These are not proper peer reviewed sources. These are books. The type of source I'm looking for is a form of a some experimental study that was conducted that confirms what you claim.
Again, neither life nor the universe itself would have existed without the fine tuned constants. This has nothing to do with some other imaginary universe that may or may not exist. the comparison is irrelevant.
Again, not a claim you can make. You'd need an example of a universe with different constants to know that for sure. Otherwise it's just an empty claim on your part.
To calculate a chance, you will need to multiply the probability of the first constant by the probability of the second and so on. The cosmological constant alone is fine tuned to “1 in 10 to the power120 ”. The probability of all the constants to be collectively fine tuned at the same time will be extremely small to an unimaginable extent.
To calculate a chance, you need to know all possible configurations. For instance, with a die, it has six sides, so it landing on any particular side is 1/6. For a coin, it's 1/2. For ten dice, it's 1/60466176. To say the configuration of our universe is vanishingly small, you need to know all possible configurations of universes. But you don't. What you have is an unknown amount of dice with an unknown amount of sides. Thus, an unknown probability for any particular configuration. For all you know, this universe is the only possible configuration.
Additionally, you have an unknown amount of allowed attempts at throwing the dice. The more allowed attempts, and the greater the probability of any specific configuration eventually coming up. If the allowed attempts are limitless, then any otherwise improbable configuration, suddenly becomes guaranteed.
The Universe has been here a very long time. It's spawned countless planets, the vast majority of which don't have life. You can consider each lifeless planet as the universe's attempt at throwing the dice, and failing each time, until it finally made Earth.