The arguments relating to the fine-tuned universe concept are related to the anthropic principle, which states that any valid theory of the universe must be consistent with our existence as human beings at this particular time and place in the universe. In other words even though the actual probability of a universe to be one which supports intelligent life is very low, the conditional probability given our existence in it is 1 - and even if there are other universes devoid of life, there will be no one to observe them.
The premise of the fine-tuned universe assertion is that any small change in the approximately 26 dimensionless fundamental physical constants would make the universe radically different: if, for example, the strong nuclear force were 2% stronger than it is (i.e. if the constant representing its strength were 2% larger), diprotons would be stable and hydrogen would fuse into them instead of deuterium and helium. This would drastically alter the physics of stars, and presumably prevent the universe from developing life as it is currently observed on the earth.
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