2
$\begingroup$

$34$ of the $109$ nurses are male. If $26$ nurses are randomly selected from those employed by the hospital, what is the probability that the sample of $26$ will include exactly $15$ male (and $11$ female) nurses?

The way I was thinking about this was like this:

For finding males:

$$\frac{\binom{26}{15}}{\binom{109}{34}},$$

for finding females:

$$\frac{\binom{26}{11}}{\binom{109}{75}}.$$

I am not 100% sure is this is the correct or not.

$\endgroup$
  • $\begingroup$ You are not choosing the 15 males from a population of 26, you are choosing 15 males from a population of 34 (and similarly for females) $\endgroup$ – David Peterson Feb 13 '14 at 6:48
4
$\begingroup$

It is

$$\dfrac{{34\choose 15}{75 \choose 11}}{{109\choose 26}}\approx 0.001$$

$\endgroup$

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.