Question 62835
<b>Four cards are numbered 1 through 4. Two of these cards are chosen at random without replacement and the numbers on them are multiplied. Find the expected value of this product.</b>

There are 12 possible outcomes when you draw two cards because there are 4 ways to draw the first cards then there are 3 cards left thus 3x4 total ways to draw the cards.

Let's enumerate the possible outcomes. They are:
{1,2}{1,3}{1,4}{2,1}{2,3}{2,4}{3,1}{3,2}{3,4}{4,1}{4,2}{4,3}

Let's now enumerate the product of the numbers:
2,3,4,2,6,8,3,6,12,4,8,12

To get the expected value we multiply the products we just listed with their probabilities, which is 1/12 for each and add up these numbers.

So, the expected value = {{{(2+3+4+2+6+8+3+6+12+4+8+12)/12 = 70/12}}} = {{{highlight(5.8333)}}}.