# Simple Probability question

by the riddick25
Tags: probability, random walk
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,340 Simple Probability question This is a binomial distribution with p= q= 1/2 and so will involve $(1/2)^{20}$. Let n be the number of forward steps he took. Then 20- n is the number of backward steps. Assuming he started at the door, if he is 14 steps back into the pub, taking forward steps positive and backward steps negative, we must have n- (20- n)= 2n- 20= -14. Solve that for n. Now that you know the number of forward and backward steps, you can use the binomial coefficient to determine in how many orders he could have taken those forward and backward steps. (By the way, I find this problem, and any problem postulating people not in control of themselves, offensive.)