The very first episode of Stats for Geeks’ podcast answers the question: What’s the danger of pulling three poisonous Skittles out of a bowl?

Notes:

The formula below shows the probability of pulling all three poisonous Skittles out of a bowl of 25 Skittles:

$$(\frac{3}{25})\times(\frac{2}{24})\times(\frac{1}{23})=0.04$$

The formulas below show the probability of getting all three poisonous Skittles when pulling 10 out of a bowl of 25 Skittles and the probability of getting one poisonous Skittle when pulling 10 out of a bowl of 25 Skittles.

$$\frac{\begin{pmatrix}3\\3\end{pmatrix}}{\begin{pmatrix}25\\10\end{pmatrix}}$$

$$\frac{\begin{pmatrix}3\\1\end{pmatrix}}{\begin{pmatrix}25\\10\end{pmatrix}}$$