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Math Question on Expected Value?

Ten cards are numbered 1 through 10. Two of these cards are chosen randomly(without replacement) and the numbers are then added. Find the expected value of this sum.

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  • 8 years ago
    Favorite Answer

    There are 90 combinations: (1,2), (1,3), ..., (1,10), (2,1), (2,3), ..., (2,10), ..., (9,10). The expected value is:

    [ (1+2)+(1+3)+...(1+10) + (2+1)+(2+3)+...+(2+10) + ... + (9+10)] / 90

    = [ 3+4+...+11 + 3+5+...+12 + ...] / 90

    = [ 63 + 71 + 79 + ... + 135 ] / 90

    = 990 / 90

    = 11

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