Question

Six cards are numbered 1,1,6,7,11 and 12. Cards are chosen, without replacement, until a card numbered 1 is chosen. Find the probability that this happens before the third card is chosen.

Answer 1

This can be found from the hypergeometric distribution as follows:
\[P(X=1)=\frac{\left(\begin{matrix}2 \\ 1\end{matrix}\right)\left(\begin{matrix}4 \\ 1\end{matrix}\right)}{\left(\begin{matrix}6 \\ 2\end{matrix}\right)}=\frac{16}{30}\]