I need solution for this problem ASAP. Probability problem with two arrays of holes.

#1
Given two arrays of holes, Each hole can be filled in by a white ball or a black ball.
1. Each array has n holes, and can be filled in by r black balls and (n-r) white balls.
2. Both arrays are filled independently.
3. Both arrays have been indexed by the same set of integers 1,2,3,...n. We say positions 1,2,3,...n.
4. Let x be the number of positions being filled by at least one black ball.
5. Let y be the number of positions being filled by both black balls.
Let p be a number where 1 <=p<=n. Work out the probabilities P(x>=p) and P(y>=p) for any p.
Could be in two steps; Firstly, let r<n/2, secondly let r<n.

Thank you in advance.
 
Last edited:

BGM

TS Contributor
#2
Re: I need solution for this problem ASAP. Probability problem with two arrays of ho

So in the problem set up you have infinitely many white balls and black balls? Or just a finite number of them? (say a total of \( n \)?)
 
#3
Re: I need solution for this problem ASAP. Probability problem with two arrays of ho

As per the description of the problem, I think, only a total of n balls.