Amazing twisting probability problem

[tawdry cliff]

there is only 1 way to make them not intersecting

[pliant ice]

If they are not parallel they will always intersect, so I guess 100%

[atomic rover]

Plot twist: The problem is set in hyperbolic space.

[gleaming condor]

2 ways

I think the probability will be infinitesimally close to 100% but not exactly there

[lavish frost]

I'm not sure, but I would say 100%, because there are only two cases where the tangents don't intersect and inifnite cases where the tangents intersect.

[tawdry cliff]

nvm 4 ways

its a percentage that approaches 100% but not 100%