Question 62835: 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.
Answer by joyofmath(189)   (Show Source):
You can put this solution on YOUR website! 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.
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 =  =  .
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