[VA] SRC #012a - Then and Now: Probability

[C.Ret]

Hi there,

Just three small questions that I ask everyone to confirm that I have understood the problem and not read it too quickly - I have this bad habit -.

           7        
          / \       
         1 ─ 2      
        / \ / \     
       6 ─ A ─ 3    
      / \ / \ / \   
     . ─ 5 ─ 4 ─ .  
    / \ / \ / \ / \ 
   . ─ . ─ 8 ─ . ─ .

From point A, a step can only lead the man only to points 1 2 3 4 5 and 6. To go to points 7 and 8, you need at least two steps by passing through one intermediate points?


My program finds that on a triangle of R=5 rows, the probability that the man is on the last row after S=4 steps is P ~ 0.07961.
Is this a correct value?

On this same triangle R=5, my program finds a probability P ~ 0.1766 that the man is on the last line after S =7 steps.
Does this seem possible to you?

EDIT:
I upgraded my code to avoid rounding errors as much as possible.
Now I find P = 1656 / 20736 for R=5 and S=4 and P = 6329160 / 35831808 for R=5 and S=7.