Problem:
Three balls marked and are placed in an urn. One ball is drawn, its number is recorded, and then the ball is returned to the urn. This process is repeated and then repeated once more, and each ball is equally likely to be drawn on each occasion. If the sum of the numbers recorded is , what is the probability that the ball numbered was drawn all three times?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A total of can be achieved by equally likely ordered triples of draws: and .
Therefore the answer is .