A variation of the Ehrenfest model of diffusion was studied in Section 10.2, Exercise 33. Consider this model with k = 3 and p = 1/2 and suppose that there are now 3 molecules in urn A. How many draws on average will be needed until there are again 3 molecules in urn A?

Data From Section 10.2 Exercise 33

Consider the variation of the Ehrenfest urn model of diffusion studied in Section 10.1, Exercise 33, where one of the 2k molecules is chosen at random and is then moved between the urns with a fixed probability p.

Data From Section 10.1 Exercise 33

Another version of the Ehrenfest model for diffusion starts with k molecules of gas in each urn. One of the 2k molecules is picked at random just as in the Ehrenfest model in the text. The chosen molecule is then moved to the other urn with a fixed probability p and is placed back in its urn with probability 1– p.