0
$\begingroup$

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!

$\endgroup$
  • $\begingroup$ 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
0
$\begingroup$

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 $\frac{{N-m}\choose{k}}{{N}\choose{k}}=\frac{{429-29}\choose{27}}{{429}\choose{27}}=0.1420$

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.