I have 5 marbles numbered 1 through 5 in a bag.  Suppose I take out two different marbles at random.  What is the expected value of the product of the numbers on the marbles?  Answer as a decimal to the nearest tenth.
There are $\binom{5}{2} = 10$ different pairs of marbles that can be drawn, and the expected value of the product is the average of the products of each pair.  This is  \begin{align*}
\frac{1}{10}[(1\times 2)&+(1\times 3)+(1\times 4)+(1\times 5)+{}\\
&(2\times 3)+(2\times 4)+(2\times 5)+(3\times 4)+(3\times 5)+(4\times 5)]\\
&\qquad\qquad\qquad\qquad=\frac{85}{10} = \boxed{8.5}. \end{align*}