8 Three balls are divided between two containers. During each period a ball is randomly chosen and switched to the other container.

a Find (in the steady state) the fraction of the time that a container will contain 0, 1, 2, or 3 balls.

b If container 1 contains no balls, on the average how many periods will go by before it again contains no balls? (Note: This is a special case of the Ehrenfest Diffusion model, which is used in biology to model diffusion through a membrane.)