In a box there are 15 tennis balls of which 9 have never been
used. Three balls are chosen at random, played with them and at the
end of the balls they are returned to the box. The next day three
balls are again selected at random from the box. [Show your results
to at least four decimal places.]
a) Find the probability that none of these 3 balls have been
used before. [Hint: consider the total probability theorem.]
b) If you know that the three balls of the second day are new,
what is the probability that in the game of the previous day two of
the three balls have already been used?