Answer
$\frac{1}{100,000,000}$, doesn't seem feasible.
Work Step by Step
There are 100 numbers, so by using the fundamental counting rule we can get the number of possibilities: $100\cdot100\cdot100\cdot100=100,000,000$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{100,000,000}$. This is a lot of opportunities, so it is doesn't seam feasible to open the safe with random tries.