I haven’t written anything in a while, and I thought tonight was a good night to write. Something interesting happened today while I was in the elevator and I thought I’d share it here with you all :p
Seriously if you think this is boring, either skip to the last two sentences or type http://youtube.com in your address bar, I hear they have interesting videos on that site. Come to think of it, here’s a quick story: My cleaning lady likes to talk, and yesterday she was talking about youtube and how she loves it and the first time she saw it etc.. Now she’s a bit old and not tech-savy, yet she was tell me how she felt the first time her daughter showed her youtube. She described her feelings as if this youtube site was invented before world war 1. Then I started to recall when I first saw youtube. I remember I read an article about it on slashdot around May or June 2005 (it was our digg/reddit back in the day). I saw the site, and I believe it was during its first or second month, and there were less than a thousand videos. You could have literally browsed through all the videos in a day. I remember thinking to myself, that this was a very stupid idea because streaming videos costs money, and how could they pay for all that bandwidth..? Ads? Who could manage such a global ad system? It turned out google had the power to create a global ad system so powerful, it actually made youtube work and become a billion dollar investment. Why am I talking about youtube? this is supposed to be about elevators…
Okay back to my elevator story. So I get on the elevator today around 6pm, and there are 5 people. I look at the board, and 5 buttons are pressed. After I got off on my floor, I was talking to my neighbor about the probability of each person getting of on a different floor. Its not really that rare, because the probability was 0. 25 (I’ll show you how to calculate it).
So my neighbor goes on to tell me that last week he was the tenth person to get on the elevator from the garage in our building. Each person went to a different floor, and one of them actually got off on the ground floor, which is uncommon. So, I started to think to myself, how rare is that? 10 people get on the elevator in the basement, and all go to 10 different floors in a 10 story building? The answer is 3 in 10,000..! Ok, then I started to think, how many times has this elevator had exactly 10 people in it? Our building is only 35 months old. If we assume that the elevator gets exactly 10 people going up from the basement floor(s) in it, 4 times a day during the weekdays and twice during saturdays and sundays, and I do believe that I’m pushing it there. That would mean that since the building was built until today, this has only happened 3639 times at most.
So, the probability that this has ever happened in our building is 0.36, which means there is a 0.636 chance that this has never ever happened..! And if it did happen, then it would have been a very very rare occurrence…! I sorta wish I was on that elevator…
Okay to calculate the probability, you do the following:
- First person will obviously push an un-pressed button: probability is 10/10 = 1
- Probability of the second person pressing one of the un-pressed buttons: 9/10 = 0.9 (there is a 0.1 chance he’ll push the one pressed by the first guy)
- Probability of the third person pressing one of the un-pressed buttons: 8/10 = 0.8 (again there is a 0.2 chance he’ll push a previously pressed button)
- Probability of the forth person pressing one of the un-pressed buttons: 7/10 = 0.7
- Tenth guy pressing the last un-pressed button: 1/10 = 0.1 (meaning there is a 0.9 chance he’ll press a button already chosen by someone else!)
Total probability is the product of all the probabilities = 1 * 0.9 * 0.8 * 0.7 …. * 0.1 = 0.00036288
which means this only happens 3 or 4 times every 10 thousand times!
obviously this was the case for our building, and it might be different for yours, but at least now you know how to calculate it. I wonder if anyone actually read this.. LOL