(solution) The town of Mythica has a “free bikes for the people program.” You can pick up bikes at the…

(solution) The town of Mythica has a “free bikes for the people program.” You can pick up bikes at the…

The town of Mythica has a “free bikes for the people program.” You can pick up bikes at the library (L), the coffee shop (C), or the cooperative grocery store (G). The director of the program has determined that if a bike is picked up at the library ends up at the coffee shop with probability 0.2 and at the grocery store with probability 0.3. A bike from the coffee shop will go to the library with probability 0.4 and to the grocery store with probability 0.1. A bike from the grocery store will go to the library or the coffee shop with probability 0.25 each. On Sunday there are an equal number of bikes at each place. (a) What fraction of the bikes are at the three locations on Tuesday? (b) On the next Sunday? (c) In the long run what fraction are at the three locations?