You’re down into single digit percentage by the time n hits 7 in that case. What are we at, 4th re-entry? So 25% chance it lands in water given your formula. Given Chinese superstitions around the number 4, let’s hope this one has a safe and wet splashdown.

That’s not how the stats work. There’s a 71% chance it lands in water this time (and every time). If you flip heads 3 times in a row, it doesn’t mean you’re more likely to flip tails next time.

My understanding is that this is more of the equivalent of making sure you land on heads all 3 times. In that case it’s a 1/8th on 3 coin flips, no?

> My understanding is that this is more of the equivalent of making sure you land on heads all 3 times

Yep!

That's a five year-olds uninformed take because you assume it could land anywhere on earth, hence 71% water....

Orbital mechanics does not work that way (except for a polar orbit). It's covering a particular band of the surface that it could land on if uncontrolled.