With replacement, tree branches into 4 paths then 4 paths each, creating 16 pairs (size 16). Without replacement, first draw branches into 4 paths then 3 paths each, creating 12 pairs (size 12).
A box contains 4 balls numbered 1 to 4. Record a sample space using a tree diagram for the following experiments: (i) A ball is drawn and the number is recorded. Then the ball is returned and a second ball is drawn and recorded. (ii) A ball is drawn and recorded. Without replacing the first ball, the experimenter draws and records a second ball. (iii) What are the sizes of these two sample spaces?
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