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Let denote the value on the
-th drawn ball. We want to find the expectation of
, which by linearity of expectation is
(which is true regardless of whether the are independent!)
At any point, the value on any drawn ball is uniformly distributed between the integers from 1 to 10, so that each value has a 1/10 probability of getting drawn, i.e.
and so
Then the expected value of the total is