The Inspection Paradox Explained (Waiting Time Paradox)

[@scoreunder]

I'm mildly jealous at the assertion that buses come once every 10 minutes. I want to live wherever that place is lol

[@richardbloemenkamp8532]

It is the case here in Paris, France and probably in other larger cities as well. I still prefer metros which are more frequent.

[@rodge4411]

I love this. The last distribution is not a bad model for the trains in my city (where there are frequent problems). If I see the platform empty, I know I just missed a train but at least the trains are running!

[@lionhawk555]

You present two cases - just missing a bus, and not just missing a bus. But in real life there are three cases. Just missing a bus, arriving when you can see a bus approaching, and arriving when there is no bus in sight. Does this affect the calculation?

[@jauchi5078]

so if i understand it the right way it all depends on the variance of time between busses arriving, doesnt it? If there was no variance, the t/2 statement should be true, the higher the variance gets to more inacurate the intuition gets, right?

[@MrRyanroberson1]

To play off the students example: if you sample every time that is just a couple seconds after each minute mark, you get 10 1-minute waits, 10 2-minute waits... 10 5-minute waits, 9 10-minute waits, and another 8 waits that are longer than that. Averaging them all gives a wait time of 14.8 minutes, which I find to be slightly more paradoxical than the fact that a totally random distribution expects a slightly shorter wait time than this

[@harper8042]

the paradox can be made compatible with intuition if you just push the 50 minute bus scenario to an extreme :) imagine a bus schedule where a thousand buses arrive one microsecond after the other, and the 1001st bus arrives one whole second after the 1000th bus. now we have on average one bus every millisecond but an inspector can expect to have to wait around half a second to see a bus obviously pushing it with the bus schedule example but the principle is the same

[@coreymonsta7505]

What’s inside of your set B?

[@DrBarker]

I think of it as maybe representing a ball!

[@grantofat6438]

If busses leave every 10 minutes, I usually have to wait about half an hour for the next one. That is called reality.

[@yulinliu850]

Thanks!

[@worldnotworld]

Funny, I don't find this counterintuitive at all! The "just missed the bus" scenario will land you on the 50 minute bus happen only one out of ten times, where as showing up randomly will land you there half the time.