So I was leaving work today when something interesting happened… I got in the elevator, and there was a girl in there. She anxiously checked her phone while we waited for the elevator to descend. Another guy got in before we got there, and the three of us waited for that door to open at the ground floor. When it did, the guy walked to the right, to the north exit of the building. I then did the gentlemanly thing to do and let the girl exit the elevator ahead of me. She walked to the left, to the south exit of the building, where I was also going. We went through both sets of doors, and she turned to the right to walk west down the street, the same direction I was planning on going. Maybe I’m paranoid, but after about a half of a block I noticed that she stopped, paused, looked around, and allowed me to pass, and in my paranoid mind this is because she got the feeling that I was following her.
Now this isn’t the first time that this has happened (not the same girl other times), and I’m sure it won’t be the last, so I started thinking about this mathematically. My statistics are a bit rusty (maybe someone can remind me what operation would solve this), so I relied on scripting out a brute force solution:
Assuming there are four exits to the building, what is the probability that at least one other person in the elevator with this girl will choose the same exit as her?
Running this a few times, I got these results:
Would you look at that! It seems that with only 3 more people in the elevator, it is actually more likely than not that one of them will go out the same exit as her!
These ladies leaving their work places should stop being paranoid that someone is following them!
(a more likely conclusion: this whole scenario occurred entirely in my head and I am the one who should stop being so paranoid!)