0
$\begingroup$

I have a question about probability that seems to be more difficult than I thought:

We assume we have a set of $x$ balls: all of them are white except one that is black ($x-1$ white ball and $1$ white ball)

We take $4$ balls from the set at once. Would please help me calculate the probability that this set contains the black ball?

Thanks!

$\endgroup$
0
$\begingroup$

HINT: Calculate the probability that it does not contain the black ball, and subtract from $1$. How many $4$-ball sets are there that do not contain the black ball? How many are there altogether?

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ So,you propose: $P(black ball)=1-C_{4}^{x-1}$, right? $\endgroup$ – ra7ma Nov 15 '13 at 15:25
  • $\begingroup$ @ra7ma: No, because $\binom{x-1}4$ can’t be a probability. Try $$1-\frac{\binom{x-1}4}{\binom{x}4}\;.$$ $\endgroup$ – Brian M. Scott Nov 15 '13 at 20:18
  • $\begingroup$ Thank you Brian, I understand it now. $\endgroup$ – ra7ma Nov 18 '13 at 15:49
  • $\begingroup$ @ra7ma: You’re welcome. $\endgroup$ – Brian M. Scott Nov 18 '13 at 15:50

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.