Probability two people wear the same shirt

[Guy Incognito]

So a couple days ago three people all showed up to work wearing the same shirt. At first I thought this was just like the birthday problem, the probability at least 2 people in a room have the same birthday, but when I think more about it I think it's different. In the birthday problem, everyone chooses a birthday from the same 365 days. They all have the same sample space.

In this shirt problem, let A=all the shirts that exist, B=the shirts person 1 owns, and C=the shirts person 2 owns. B and C will be subsets of A, but they may or may not be disjoint from each other. So when person 1 and 2 get up in the morning, they are likely sampling from different sample spaces.

Does what I say make sense? So how would you find the probability at least two people show up with the same shirt?

 

[CRGreathouse]

Does what I say make sense? So how would you find the probability at least two people show up with the same shirt?

Sure it makes sense. Usually you don't have nearly enough information to analyze it like that, though -- unless you know what shirts everyone owns. Unless you do I'd treat it like a variant on the birthday problem just as you said.

 

[robert Ihnot]

I was surprised in the washer repair business, how a certain part like a switch would hardly ever go bad; but sometimes when it did, we would get two or three such cases at the same time. Must have had something to do with the weather?