Probability - Conditional Probability

[AsianMan]

There are 15 tennis balls in a box, of which 9 have NOT previously been used. Three of the balls are randomly chose, played with, and then RETURNED TO THE BOX. Later, another 3 balls are randomly chosen from the box. Find the probability that none of these balls has ever been used.

Seems pretty simple, right?

Attempted Solution:

Event A - 1st round balls have never been used before
Event B - 2nd round balls have never been used before

We want the probability of events A and B both occurring.

Prob(A and B) = Prob(B given A) * Prob(A)

Prob(A) = (9C3)/(15C3) = 84/455

Prob(B given A) = (6C3)/(15C3) = 20/455

Prob(A and B) = .008114962



Book says answer is .0893

EDIT: I got it now. I misunderstood the question.

 

[kurt.physics]

It's asking for the probability that all 3 balls in the SECOND round have never been used. So, the correct answer is:Probability = (6C3)/(15C3) = 20/455 = .04396