Question

There are 15 tennis balls in a box, of which 9 have not previously been used. Three of the balls are randomly chosen, 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.

Answer 1

probability will be become two by three

Answer 2

Answer:

Probability that none of these balls has ever been used ≈ 0.0893

Step-by-step explanation:

1. Probability to choose 3 not previously used balls from 15 when 9 are not previously used:

$=\frac{9\times 8\times 7}{15\times 14\times 13}$

2. Conditionally on this, probability that these 3 balls were not played with because they would have been chosen in the first phase :

$=\frac{12\times 11\times 10}{15\times 14\times 13}$

Thus, the desired probability is

$=\frac{12\times 11\times 10\times 9\times 8\times 7}{(15\times 14\times 13)^2}\approx 0.0893$.

Hence, the probability that none of these balls has ever been used ≈ 0.0893