Well for n=1, the answer is 50%. For n=2, the answer is... still 50%, if my math is correct (and it's 3 AM so it may well not be; I was using 1 = 1 ft). For n=3, it's... still 50%.

For n=2, if 1 foot (12 inches) is the unit of measurement, then line 2 (L2) would be divided into 3 segments of 8 inches each. The first 8 inches would match, the next 4 wouldn't, and then 4 would match, and then the last 8 wouldn't. For n=3, the matching-unmatching inches of each foot (one segment in L1) would be, as far as I can tell, 9-3, 6-6, 3-9.

So my rudimentary guess would have to be 50%, but I am way too exhausted to try to figure out exactly why.

Math is fun. We need more math threads.