Johnson Medical Associates has two physicians on call, Drs. Dawson and Baick. Dr. Dawson is available to answer patients’ calls for time periods that are exponentially distributed with mean 2 hours. Between those periods, he takes breaks, each of which being an exponential amount of time with mean 30 minutes. Dr. Baick works independently from Dr. Dawson, but with similar work patterns. The time periods she is available to take patients’

calls and the times she is on break are exponential random variables with means 90 and 40 minutes, respectively. In the long run, what is the proportion of time in which neither of the two doctors is available to take patients’ calls?