Talk:Linear Algebra/Topic: Markov Chains/Solutions

A man either drives his car or walks in going from his home to his office in the morning, and from his office to his home in the afternoon. He uses the following strategy: If it is raining in the morning, then he drives the car, provided it is at home to be taken. Similarly if it is raining in the afternoon and his car at his the office, then he drives the car home. He walks on any mornings and afternoons that it is not raining or the car is not where he is. Assume that, independent of the past, it rains during successive mornings and afternoons with constant probability (p). Write down probability Matrix Marko chains and then: 1. In the long run, on what fraction of days does our man walk in the rain? 2. What if he owns two cars?