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A drunk person wonders aimlessly along a path by going forward 1 step and backward 1 step with equal probabilities of ½. After 10 steps,

a) what is the probability that he has moved 2 steps forward?

b) What is the probability that he will make it to his front door within 20 steps before he collapses with the door being 6 steps in front of him.

My approach was to use Binomial in both cases:

a)10C2 (0.5)^10

b)20C6 (0.5)^20

Is that correct? I have been reading about random walk and they sometimes give another equation.

(10+2)/2=6 and thn the result is like this 10C6.

The result is not the same and then I start to have my doubts.

Can some one please tell me if my approach using binomial distribution is right?