theres a cliff, standing on the edge is a man who is drunk and will be drunk forever?

Question

theres a cliff, standing on the edge is a man who is drunk and will be drunk forever and can live forever if he staggers forward he will fall to his death, if he falls backwards he will be a step closer to safety. now if the chance of him staggering forward is one third and the chance he staggers backwards is two thirds what is the chance he will eventually fall off the cliff?

Answer 1

Between 1/3 and 2/3 chance
Chance of him on his first step 1/3.
Chance if he first steps back,= 2/27 - 2/3 x 1/3 x 1/3 (ie he has to take 1 step back, then two forward to fall off cliff).
Chance if first two steps back then three
steps forward = 4/243

So its1/3+2/27+4/243 etc etc

The other options just keep adding up.

The increments get smaller, but they keep adding on to the probability.

Answer 2

this totally depends on which way the drunk is facing..if hes facing side on to the cliff then the answer is nil chance of falling off the cliff because he has 1/3 chances of going forward or 2/3 chances of going backwards which leaves no chances of going sideways.

should a gust of wind pick him up and throw him off the cliff the chances of him dieing are NIL because as u said..."he lives forever"

Answer 3

"In mathematics and physics, a random walk, sometimes called a "drunkard's walk," is a formalisation of the intuitive idea of taking successive steps, each in a random direction.

The expected number of steps until a one dimensional random walk goes up to 'b' or down to '-a' is 'ab'. The probability that the random walk will go up to 'b' steps before going down 'a' steps is a/(a+b)"

This, and more, available on the free, online encyclopedia, Wikipedia at:
http://en.wikipedia.org/wiki/Random_walk

Hope this helps!

Answer 4

one third that he will fall but if he can live forever he will not die

Answer 5

ONE (Since he can live forever)