Jelly, 7 bytes (non-competing)
‘⁵XỊ¤¿+
How it works
‘⁵XỊ¤¿+ Main link. Arguments: n, m (integers)
¤ Combine the three atoms to the left into a niladic chain.
⁵ Yield 10.
X Pseudo-randomly generate a positive integer not greater than 10.
Ị Insignificant; test if the generated integer is 1 (or less).
¿ While chain yields 1:
‘ Increment n.
+ Add m to the result.