# Probability two people wear the same shirt

1. Oct 18, 2007

### 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?

2. Oct 18, 2007

### CRGreathouse

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.

3. Oct 31, 2007

### 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?