If it takes 30 seconds on average to find a share, by the definition of an average, the distribution of "made it" or "didn't make it" when 30 seconds is the cut-off is evenly distributed between < 30 and > 30.
I have the actual odds in my post
0: 0.3673
1: 0.3685
2: 0.1842
3: 0.0612
4: 0.0152
5: 0.0030
6: 0.0005
7: 0.0001
8: 0.0000
So, 37% of the time you get nothing, 37% of the time you get 1 block and 26.5% of the time you get 2 or more. However, you get 1 block on average.