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Find the exact formula for P(Sn=k)

  1. Oct 23, 2013 #1
    A box contains four tickets, numbered 0,1,1, and 2. Let Sn be the sum of the numbers obtained from n draws at random with replacement from the box.
    Find the exact formula for P(Sn=k) (k=0,1,2....)

    I started by finding the probability of the first few sums:
    P(Sn=0) = (1/4)^n
    P(Sn=1) = n * (1/4)^(n-1) * (1/2)
    P(Sn=2) = n * (1/4)^(n-1)*(1/4) + (n choose 2) * (1/4)^(n-2)(1/2)^2

    Then I get stuck, since the combinations of draws that lead to the subsequent draws get much more complicated.
    Is there a more simplified way to find the formula for P(Sn=k)?
  2. jcsd
  3. Oct 24, 2013 #2


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