In my perception, using the common sense, is less common, or less probable, to a random line be parallel that not to be, because to be parallel a line needs obey a restrictive rule. But anyone can, using simple probability, obtain that result:
specific line (r) = any line in R2 (e.g. y=0) amount of random lines (u) = infinite (inf) amount of parallel lines to r (s) = infinite (inf) probability of s parallel to r = s / u = inf/inf = undefined
But there is another solution? Maybe using geometric probability, integrals or even empirical results?
[EDIT]
OK. I've understood the zero result and the "not impossible" thing. Thanks for answers and references.
But...
- Is my initial perception wrong?
- Is not easier to find a not parallel line instead a parallel?
- Could someone prove or negate it?
- If my perception is not wrong someone can calculate how easier is?
- or maybe I really didnt understand the answers?
[NEW EDIT] So, is it the final answer? - Is my initial perception wrong? - A: No, its correct.
- Is not easier to find a not parallel line instead a parallel?
A: Yes, it is easier.
Could someone prove or negate it?
A: Yes: '''The probability of finding a parallel line is zero, so the probability of finding a non-parallel line is equal to one. Since 1>0, you have the answer to your question. – Rod Carvalho'''
If my perception is not wrong someone can calculate how easier is?
- A: No, nobody can because it is undefined. (?)
[FINAL EDITION]
Now I realize that the question resumes to: which is the probability of a random real number be equal to a specific other. Thanks for help.