Random Walk decided by a coin

Question

It's a discrete math question, so hope it's okay to post here. I have this lattice graph, where you start at Z and have to end in one of the S. You can only go down (so all the lines are actually down arrows), and every walk has to end in one of the S. The way you go (left or right) is decided by a coin. I have to calculate the probability of the chance that a walk ends in the different S's. I have figured out that there is only one way to get to S0 and S6, so the probability would be:

$(1/2)^6 = 0,0156$

So my question is, how do I calculate the probability of the other S's? (I have also a normal picture of the lattice graph if needed)

             Z
            / \
           Y0 Y1 
          / \ / \
         X0  X1 X2
        / \ / \ / \
       W0  W1  W2 W3
      / \ / \ / \ / \
     V0  V1  V2  V3 V4
    / \ / \ / \ / \ / \
   U0  U1  U2  U3  U4  U5
  / \ / \ / \ / \ / \ / \
 S0 S1  S2  S3  S4  S5  S6

Answer 1

Let's start with the X row. The number of ways to get to X0, X1 and X2 are 1,2,1.

For the W row it's 1,3,3,1. Try and find them.

For each row it's the numbers in Pascals triangle (look this up if you aren't used to it). So for the S row it's 1,6,15,20,15,6,1. Since they add up to 64 the probabilities are $1/64, 6/64, 15/64 $, etc...