1. Suppose that, during a long winter, every time it snows today, it snows to- morrow with probability 0.7. Every time it does not snow today, it snows tomorrow with probability 0.3. On days when it snows, an individual has a probability of 0.8 of wearing a hat, whereas if it is not snowing the individual wears a hat with probability 0.1. What is the proportion of days that the individual wears a hat throughout the winter