Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Random walk or binomial?

  1. May 7, 2013 #1
    Random walk or binomial??

    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?
  2. jcsd
  3. May 7, 2013 #2


    User Avatar
    Science Advisor

    Hey marina87.

    I think you should retry your problem by defining a sum of random variables with P(X = 1) = P(X = -1) = 1/2.

    A binomial random variable only includes 0 and 1 where as it should include -1 and 1.

    You can then use a probability generating function to get the probability of having a final sum of +2.
  4. May 8, 2013 #3
    Your method works fine, except I think part b) is answering the wrong question. If the drunk ever gets to +6, then he goes inside and stops walking. I think your answer to b) is the number of paths which end at +6. This neglects any paths which get to +6 at some time ##t<20##, but then end up somewhere else at ##t=20##.

    If I understood the question right, this is a famous hitting time problem. I had to solve a related problem in a stats class, and I still have to think about it a while to do it right. Spoilers: click here and scroll down to "The Maximum Position."
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook