Q: Find Probablity Mass Function of Opening Boxes 
There are 5 closed boxes on the table. 3 of the boxes have prizes, the other 2 do not. You open boxes one at a time until you find a prize. Let $X$ be the number of boxes you open.
Find the probability mass function of $X$.

$X\in\{1, 2, 3\}$
$P(X=1)=\frac{3}{5}$
$P(X=2)=\frac{2}{5}\cdot\frac{3}{4}$
$P(X=3)=\frac{2}{5}\cdot\frac{1}{4}\cdot\frac{3}{3}$
$P(X=x)=$ ?

A: You are done.
$$P(X=x) = \begin{cases}\frac{3}{5}, & ,x=1 \\
\frac{2}{5}\cdot\frac{3}{4}, & ,x=2\\
\frac{2}{5}\cdot\frac{1}{4}\cdot\frac{3}{3}  & ,x=3\\
0, & \text{,Otherwise}\end{cases}$$
