<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] $$\frac{\frac{C\left( \begin{matrix}
   5  \\
   5  \\
\end{matrix} \right)}{C\left( \begin{matrix}
   10  \\
   5  \\
\end{matrix} \right)}}{\frac{C\left( \begin{matrix}
   5  \\
   3  \\
\end{matrix} \right)C\left( \begin{matrix}
   5  \\
   2  \\
\end{matrix} \right)+C\left( \begin{matrix}
   5  \\
   4  \\
\end{matrix} \right)C\left( \begin{matrix}
   5  \\
   1  \\
\end{matrix} \right)+C\left( \begin{matrix}
   5  \\
   5  \\
\end{matrix} \right)C\left( \begin{matrix}
   5  \\
   0  \\
\end{matrix} \right)}{C\left( \begin{matrix}
   10  \\
   5  \\
\end{matrix} \right)}}=\frac{1}{126}$$
</s>