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Related to How did Trinity know that Neo would see a white rabbit (to follow)?, how did she know that Choi (boyfriend of Du Jour, the girl with the tattoo) would invite Neo to the club?
Neo is asleep at his computer. All Trinity knows is that Choi and Du Jour are going to Neo's apartment to buy something on their way to a nightclub. Choi invites Neo on a spur-of-the-moment impulse, not as part of a plan he devised ahead of time.
Something wrong, man? You look a little whiter than usual.
NEO My computer... it... You ever have that feeling where you're not sure if you're awake or still dreaming?
All the time. It's called mescaline. It's the only way to fly. Hey, it just sounds to me like, y'know, you need to unplug, man. Y'know? Get some R&R? What do you think, Dujour? should we take him with us?
I can't. I have to work tomorrow.
Come on. It'll be fun. I promise.
Yeah. Sure. I'll go.
For Neo to go with Choi, Du Jour, and the other weirdos, several things needed to happen:
Neo has to wake up for no apparent reason when the words "Wake up, Neo" appeared (almost silently) on his screen.
Neo has to see the white rabbit and make the mental connection to the messages he received from an anonymous hacker.
The weirdos who came to buy stuff from him have randomly decide to invite him to the club where Trinity will meet him1.
Neo has to accept the invitation1, despite the facts that:
It is late at night
He was just sound asleep
He doesn't appear to be personal friends with the weirdos
He has to be at work in a few hours
Instead of freaking out because someone is spying on him, knows about his felonious behavior, and has hacked into his computer, Neo has to obey his anonymous stalker and ignore the fact that this person could get him arrested2.
Let's assume that Neo is so curious about the mysterious "Matrix" that he'd accept the invitation to the club after seeing the tattoo, and that Trinity knows this. We'll also assume that Trinity was certain that Neo would see the tattoo and make the mental connection to her message.
We're still faced with the problem of how Trinity could be sure that the weirdos would invite Neo to the club.
How did Trinity know that Choi would invite Neo to the club?
1Or alternatively, Neo has to invite himself, and the weirdos have to let him come along.
2Neo was asleep, and his computer was scanning through news stories about Morpheus, when the screen went black and a message from an unidentified person appeared - in other words, someone hacked his computer. He regularly uses this computer to commit felonies. The person who hacked his computer knows that a group of weirdos was about to knock on his door to buy illegal programs or code or whatever it was; he or she also knew that one of the weirdos had a tattoo of a white rabbit on her shoulder - in other words, whoever sent the messages is spying on Neo's apartment building right now, and knows that he has just committed another crime. If I were him, I would be destroying my computer and any other evidence of my criminal activity, not going clubbing with weirdos.