A drunkard is 9 steps away from home, and 1 step behind him is a pit. He will move 1 step forward/backward with probabilities of 0.7/0.3 respectively.What are the probabilities that
(a) he will fall into the pit
(b) reach home
(c) reach 1 step away from home
I had solved a somewhat similar problem, but with no pit and a condition of reaching home in 20 steps or less, by analysing patterns on a 2D lattice, getting the formula
sum of (3/n)*C(2n, n+3)*0.7^(n+3)*0.3^(n-3) for n = 3 to 10 = 0.814401
but i don't know how to tackle this question.
I'm not very savvy mathematically, so the simpler the explanation, the more welcome it will be !