<s>[INST] Five white balls, five black balls There are 5 white balls and 5 black balls in a box. A visually-challenged man takes 5 balls from the box... What's the probability that all the balls which this individual picked are white if we know for sure that there 3 white balls among those 5 balls he took?
Using the formula $P(A | B) = P(A \cap B)/P(B)$, I get a probability of $1/100$.
 [/INST] Your answer is correct if you are doing "three white balls among five chosen balls", but is incorrect if the problem is looking for "at least three white balls".Stricktly according to your formula, $P(A | B) = \frac{P(A \cap B)}{P(B)}$
$B=$ at least three white balls among five chosen balls,  $P(B)=\frac{\begin{pmatrix}5\\3\end{pmatrix}\begin{pmatrix}5\\2\end{pmatrix}+\begin{pmatrix}5\\4\end{pmatrix}\begin{pmatrix}5\\1\end{pmatrix}+\begin{pmatrix}5\\5\end{pmatrix}\begin{pmatrix}5\\0\end{pmatrix}}{\begin{pmatrix}10\\5\end{pmatrix}}=\frac{126}{252}$
$P(A \cap B)=\frac{\begin{pmatrix}5\\5\end{pmatrix}\begin{pmatrix}5\\0\end{pmatrix}}{\begin{pmatrix}10\\5\end{pmatrix}}=\frac{1}{252}$
So $P(A | B) =\frac{\frac{1}{252}}{\frac{126}{252}}=\frac{1}{126}$
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