Please solve it on page and shows all the steps in detail .Thank You

2. From the book Fundamentals of Probability (FOP): A box contains 18 tennis balls, of which eight are new. Suppose that three balls are selected randomly, played with, and after play are returned to the box. If another three balls are selected for play a second time, what is the probability that they are all new? Hint: Use the Law of Total Probability with the partition Bo, B1, B2, Ba, where Bi = {i new balls are selected (the first time), played with, and returned to the box} . (A) Find P(B;) for i = 0, 1, 2, 3. (B) Let A denote the event that the three balls selected the second time are all new. Find P(A| B;) for i = 0, 1, 2, 3. (C) Find the desired probability, P(A). (D) Now, assume that the balls chosen the second time were all new. What is the probability that exactly two new balls were selected the first time, played with, and returned to the box? That is, find P(By|4)