SOLUTION: An urn contains 4 balls numbered 0 through 3. One ball is selected at random and removed from the urn and not replaced. All balls with nonzero numbers less than that of the selec

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)