lets say your robot is at 0(zero) position of X axis you robot either take only one step at a time.
either left or right
what will be probability that robot is at 0 position after 1000 steps.

  brute force
  loop 0 to 1000
  math.random move left, move right

  50% chance move left, 50% move right

  simulation
  	method
    	loop 0 to 1000

  	run method 1000, 1000000x then calculate stats

  what is probability that robot is at 0 position after 4 steps
  after 1 step 0%
  	robot at -1, 1 total possibilties=2
  after 2 steps
  	robot at -2,0,0,2 total possibilties=4
  	50%
  after 3 steps
  	robot at -3,-1,-1, 1, -1, 1, 1, 3  -> 0 probability  total possibilties=8
                                    i
  after 4 steps
  	robot at -4,-2, -2,0, -2,0,0,2, -2,0, 0,2, 0,2,0, 2,4  total possibilties=16
                       1     2 3       4  5    5   7


  Hint:

      1  0   4  0 6 0 4 0 1  step 4
      0  1   0  3 0 3 0 1 0  step 3
      0  0   1  0 2 0 1 0 0  step 2
      0  0   0  1 0 1 0 0 0  step 1  ->
      0  0   0  0 1 0 0 0 0  step 0  ->
      -4 -3 -2 -1 0 1 2 3 4
  0        1     2 (2 steps)     3      4 (4 steps)
  100      0     50              0      50?
combinatorics, stats, math

  combinatorics - google - math cool question - assume that
  - how to use computer science/