Answer Happy

A hospital has 4 ventilators. All severely ill Covid patients need a ventilator. Each day, the hospital receives a new severely ill Covid patient with probability 0.2, independent of what occurs on other days. However, if all 4 ventilators are being used, the hospital turns the new patient away. Each night, each severely ill patient recovers with probability 0.1, but dies with probability 0.02, independent of the other patients. Define variables and write equations that, if solved, would give the expected number of days until the hospital turns a patient away, if initially it has two severely ill patients.