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lraines
A package contains 6 candy canes, 4 of which are cracked. If 2 are selected, find the probability of getting exactly one cracked candy cane.
This question relates to sampling without replacement. The hypergeometric distribution applies: \[P(1)=\frac{\left(\begin{matrix}4 \\ 1\end{matrix}\right)\left(\begin{matrix}2 \\ 1\end{matrix}\right)}{\left(\begin{matrix}6 \\ 2\end{matrix}\right)}=\frac{4\times 2\times 2}{6\times 5}\]
\[P(1)=\frac{4\times 2\times 2}{6\times 5}=\frac{16}{30}=\frac{8}{15}\]