# What is the probability that two samples from a source have no overlap?

I picked 29 results from a list of 429 results. I then picked a second group of 27 (with replacement) results from the same list of 429. There was no overlap between the two samples. What is the probability of this?

I'm sure it's a simple question, I know there are similar question asked, but I haven't managed to apply them to my exact question. Any help appreciated!

• Is there a typo in your question ? 429 or 492 ? – rgk Mar 15 '19 at 16:51
• Answers to this question are available by linking through the hypergeometric tag. – whuber Mar 15 '19 at 17:54

Let the initial number of results be $$N = 429$$. We draw $$m=29$$ results in the first trial. We then draw and $$k=27$$ results (with replacement). We get no 'overlap' in results if we choose the $$k$$ results from ones other than $$m$$ which is $$N-m$$
The probability that the results don't overlap is $$\frac{{N-m}\choose{k}}{{N}\choose{k}}=\frac{{429-29}\choose{27}}{{429}\choose{27}}=0.1420$$