  The wetting transition is studied in the McCoy-Wu Ising model in which the
random bonds are perfectly correlated in the direction parallel to the walls .
The model is solved numerically on finite size lattices up to $200 \times
200^2$. It is shown that the wetting transition is first-order. For a fixed
surface field, the distribution of wetting transition temperature is obtained
from $1000$ samples. The results show that the deviation of the wetting
transition temperature does not decreases as the lattice size increases. It is
shown that for a fixed surface field the wetting transition temperature is
sample dependent even in the thermodynamic limit.
