Given two arrays of holes, Each hole can be filled in by a white ball or a black ball.

1. Each array has

2. Both arrays are filled independently.

3. Both arrays have been indexed by the same set of integers

4. Let

5. Let y be the number of positions being filled by both black balls.

Let p be a number where 1

Could be in two steps; Firstly, let

Thank you in advance.

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: