On a planet away and afar

Shines a Sun which to us is a star

But only on days

And according to ways

Of numbers and systems bizarre

Letting his light shine on (call it) day one

Then day two chances one percent dawn

But if no light does shine

Then a new day unwinds

And day three chances two percent Sun

So day four chances three percent Sun

If day three had also seen none

And likewise it goes

A generalization which shows

On day chances *

If the Sun shines on day one, then what day (or days) is most likely to also see Sun and what is the probability? (approximation to several decimal places is fine)

* ** percent** ('Percent' does not rhyme with 'Sun' and 'none'.)