Beginner: 64 squares, 10 mines.
Intermediate: 256 squares, 40 mines.
Expert: 480 squares, 99 mines.

Using these statistics, we can figure out the probability on hitting mines on random clicks (assuming the player is completely unaware of numbers). The first click is never a mine, so we can throw that out. The odds of hitting a mine on the second click, therefore, is the number of mines divided by the number of remaining squares. So here are the odds of hitting mines, rounded to the hundredth of a percentage.

Beginner: 10/63 = 15.87% chance of hitting a mine on click 2.
Intermediate: 40/255 = 15.69% chance of hitting a mine on click 2.
Expert: 99/479 = 20.67% chance of hitting a mine on click 2.

Let's take it one step further, to a third click without hitting a mine.

Beginner: 10/62 = 16.13% chance of hitting a mine on click 3.
Intermediate: 40/254 = 15.75% chance of hitting a mine on click 3.
Expert: 99/478 = 20.71% chance of hitting a mine on click 3.

As you can see, random clicking in Intermediate actually turns out to be slightly less risky than in Beginner. However, Beginner is still "easier" for most people due to the small size of the board. Expert is obviously the hardest of the three.