Help Save a Frog From Being Eaten by a Poisonous Snake!
In a very large pond there are 11 lily pads in a row labeled 0 through 10. A frog is sitting on pad 1. When the frog is on lily pad N (from 1 to 9 inclusive), it will jump to pad N - 1 with probability N divided by 10, but the frog will jump to pad N + 1 with probability 1 - N divided by 10. Each jump is, of course, unaffected by previous jumps, just like flipping a coin.
Sadly, there is a poisonous and giant snake on pad 0, waiting for eternity to catch the frog; it is getting ready for a tasty snack. However, on pad 10, the frog can escape to frog paradise! You must help the frog escape by getting the answer correct for this question: what is the probability that the frog will escape from becoming morsel?
Credit is due where it is due. Thank you MAA for this awesome problem that I edited!