The first selection from {0,1,2,3} is  1/4  for each ball.  Now we need to look at what happens for each of these selections:



First           Sample space        

selection       for 2nd selection          Pr{2nd pick is 3} 

----------      -----------------          -----------------

    0              {1,2,3}                  (1/4)(1/3)

    1              {0,2,3}                  (1/4)(1/3)

    2              {0,3}                    (1/4)(1/2)

    3              {0}                      (1/4)(0)



Adding up all the probabilities for a 3 on 2nd pick:  

or about 29.2%



Check:

 The other numbers probabilities:  Pr{0} = 11/24, Pr{1} = 2/24, Pr{2} = 4/24



 Adding these should give 1:  (11+2+4+7)/24 = 24/24 = 1  (ok)



 

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