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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!

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  • $\begingroup$ Is there a typo in your question ? 429 or 492 ? $\endgroup$ – rgk Mar 15 '19 at 16:51
  • $\begingroup$ Answers to this question are available by linking through the hypergeometric tag. $\endgroup$ – whuber♦ Mar 15 '19 at 17:54
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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 $\frac{{N-m}\choose{k}}{{N}\choose{k}}=\frac{{429-29}\choose{27}}{{429}\choose{27}}=0.1420$

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  • $\begingroup$ It would help to explain the formula, for otherwise it is of little general use. $\endgroup$ – whuber♦ Mar 15 '19 at 17:55
  • $\begingroup$ Thank you very kindly for the help! $\endgroup$ – Edward Hampson Mar 18 '19 at 9:02

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