Question

1.) We have n squares that can be black or white.

2.) z of these squares are already black.

3.) Black squares can be converted to white with a probability d.

4.) Each of the z black squares has one chance to be converted to white in a single round.

5.) After a single round of this binomial sampling process, we move on to the following process.

6.) We have an urn of N balls.

7.) x of these balls are black and y are white.

8.) We are sampling from this urn without replacement.

9.) The number of balls we sample from the urn is equal to the number of squares that are not black following the aforementioned binomial sampling process.

10.) If a black ball is chosen from the urn, one of the white squares turns black.

11.) Question: What is the expected number of black squares following a round of this two-part process?

Answer 1