# Geometric distribution - or not?

Say I have 10 Boxes and there's money in one of them. For each box $i$, I get to ask if the money is inside it - what are my chances of finding the money after $k$ questions?

So, it is geometric in the sense that I keep doing the same thing until I succeed, but the probabilities keep changing. How should I look at it? The obvious answer would be $P(X=k) = 1/10-k$, but I'm not sure about it. Any hints? Thanks!

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You don't have independence here, so it's not Geometric. But things are a bit simpler. Ask yourself: what's the probability that I find the money on the first question? The second?... –  David Mitra Dec 2 '11 at 10:40
"Geometric" refers to the fact that in certain cases (not yours, as David Mitra has already pointed out) the probabilities form a geometric progression. A related question was considered a few weeks ago on stats.SE, –  Dilip Sarwate Dec 2 '11 at 12:07
You can do it in two different ways. Best is idea of @David Mitra. Long way is 1) probability get it on first try is $\frac{1}{10}$. 2) The probability you get it on second try is $\frac{9}{10}\cdot \frac{1}{9}$ (miss on first, then not miss). 3) You get it on the third try if you miss twice, then not miss. Probability is ? –  André Nicolas Dec 2 '11 at 15:44
"The obvious answer would be $P(X=k)=1/10−k$ which is not even a reasonable first attempt since all these probabilities are negative! Did you mean $1/10^{k}$ (which is still wrong except for $k = 1$?) –  Dilip Sarwate Dec 2 '11 at 17:02