Dominant genes directly linked survival?

In evolutionary theory (as far as I understand it),
1) an organism is not going to survive unless it is strong in its
daily life, and
2) dominant genes prevail, recessive genes die out.

And also, as far as I know, a mutation will only permeate throughout a
population if the organisms with the dominant genes survive to pass
them on.

Now my question is: how often is it that dominant genes are what
actually causes the organisms to survive? If it's not often, how would
a genetic mutation permeate through a population...


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