A professor has two umbrellas, each of which could either be in her office or in her car. The professor walks from her car to her office; she also walks from her office to her car. Assume that on each of these walks: It rains with probability 0.7, independently of all other walks. If it is not raining, the professor ignores the umbrellas. If it is raining, she uses an umbrella if there is one, and gets wet if there isn't. In the long run, what is the expected proportion of walks on which the professor gets wet