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 occuring.

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.

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 occuring.

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.

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