<s>[INST] What is the expected value of the product of randomly selected balls 
An urn contains four balls numbered 1, 2, 5, and 7.  If a person
  selects a set of two balls at random, what is the expected value of
  the product of the numbers on the balls?

My thoughts:
$E(X)=\sum_{k=1}^{n}a_{k}b_{k}$
$E(X) = E_{1}(X)*E_{2}(X)$
The probability of choosing the first ball is $\frac{1}{4}$, so the expected value of the first ball is $E_{1}(X)=\tfrac{1}{4}\sum(1+2+5+7) = 3.75$
The probability of choosing the second ball is  $\frac{1}{3}$(because 3 balls left after the first move). But what would be the $E_{2}(X)$, since we don't know which ball was chosen first and can't say $E_{2}(X)=\tfrac{1}{4}\sum(2+5+7)$
 [/INST] There's only 6 different ways to draw two balls, and each of those are equally likely, so I would just calculate it as:
$$
\frac{1\cdot 2+1\cdot 5+1\cdot 7+2\cdot 5+2\cdot 7+5\cdot 7}{6}
=\frac{2+5+7+10+14+35}{6}
=\frac{73}{6}
=12\frac{1}{6}
$$
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