### A debate over some simple probabilities

Posted:

**Fri Jun 01, 2007 11:12 pm UTC**I happened to visit the same restaurant twice in the same week, accompanied by different people each time. Both times it was someone else (besides me) that chose where we sat. And both times we happened to sit in the same place.

On the second visit I mentioned that we were sitting in the same place that I'd sat the last time I'd been there, and someone else asked (probably rhetorically), "What are the odds of that?"* So I said that assuming there were 50 places to sit, and assuming that our seating selection was truly random with an equal chance of sitting at any of the 50 places (which of course isn't true), then the odds were 1 in 2500.

Immediately everyone protested. My companions insisted that the odds were in fact 1 in 50 since the initial seating choice was "a given" (whatever that means). One of my friends even used an analogy, saying that by my logic, if he flipped a coin I would have a 1 in 4 chance of guessing correctly on which side it would land.

I tried to explain that while the odds of choosing correctly were 1 in 2, the odds of him flipping heads and me randomly guessing heads specifically was only 1 in 4 (and that the same was true for tails).

Another one of my companions again insisted that I was wrong, and suggested that I go back to school and take a statistics course.

So who's right here, guys?

*Addendum: We're talking about the odds of sitting in that specific place twice, which I thought was made clear by my explanation of the coin analogy, but apparently I'm biased.

On the second visit I mentioned that we were sitting in the same place that I'd sat the last time I'd been there, and someone else asked (probably rhetorically), "What are the odds of that?"* So I said that assuming there were 50 places to sit, and assuming that our seating selection was truly random with an equal chance of sitting at any of the 50 places (which of course isn't true), then the odds were 1 in 2500.

Immediately everyone protested. My companions insisted that the odds were in fact 1 in 50 since the initial seating choice was "a given" (whatever that means). One of my friends even used an analogy, saying that by my logic, if he flipped a coin I would have a 1 in 4 chance of guessing correctly on which side it would land.

I tried to explain that while the odds of choosing correctly were 1 in 2, the odds of him flipping heads and me randomly guessing heads specifically was only 1 in 4 (and that the same was true for tails).

Another one of my companions again insisted that I was wrong, and suggested that I go back to school and take a statistics course.

So who's right here, guys?

*Addendum: We're talking about the odds of sitting in that specific place twice, which I thought was made clear by my explanation of the coin analogy, but apparently I'm biased.