To Practice as a Real Estate Agent in Tallahassee, One

To practice as a real estate agent in Tallahassee, one must get a license and keep it valid. Your license expires based on how many homes you sell. Suppose that, for an agent with a new license, the time for the license to expire is an exponential random variable with mean 1/α and the time required to renew his or her license once expired is an exponential random variable with mean 1/β. Suppose that agents let their licenses expire and then renew it. If there are 12 agents at a certain agency, find the long-run proportion of time that only 2 of those agents have valid licenses.