nebulous

Why wouldn't the probability of two algorithms of different lengths appearing approach the same value as longer strings of bits are searched?

This September I'll start college aiming for a computer science degree, and I want to use the summer for self-improvement. I'm very uncertain about what skills I should try to learn, though, and recommendations would help.

[Post edited to use life expectancy data from estimated time of birth rather than from 2012 and avoid extra significant digits.] [Edited again to make the title more to the point and less abrasive, change the math since I found that Uganda is not one of their top four countries...