I am a German student who will finish his A-levels in around half a year, and for quite a long time I have this question on mind that I'm unable to find an answer to.
You have a value y=100 Now, you get a random number between 1 and 100. If the number is between 1 and 45, subtract 1 from y. If the number is between 46 and 100, add 1 to y. The game is stopped when y = 0. The random number part is now repeated infinitely, only stopped when y reaches 0.
Now, what is the probability of y ever reaching zero? Is it 1 or is it a certain percentage, and if it is, is there a way to calculate it? (Those numbers are just examples by the way, the key is just that the probability of it falling is lower than the one of it rising)
I'm really looking forward to your answers, I'm keen on finding out how this works!
The probability of ever reaching $y=0$ will be $$ \left( \frac{45}{55}\right)^{100} $$ which is about 2 chances in a billion.