Question

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.

Answer 1

This question relates to sampling without replacement. The hypergeometric distribution applies:
\[P(1)=\frac{\left(\begin{matrix}4 \\ 1\end{matrix}\right)\left(\begin{matrix}2 \\ 1\end{matrix}\right)}{\left(\begin{matrix}6 \\ 2\end{matrix}\right)}=\frac{4\times 2\times 2}{6\times 5}\]

Answer 2

right ans p(1)=8/15

Answer 3

\[P(1)=\frac{4\times 2\times 2}{6\times 5}=\frac{16}{30}=\frac{8}{15}\]