Suppose that whether it rains in Charlotte tomorrow depends on the weather conditions for today and yesterday. Climate data from 2003 show that

• If it rained yesterday and today, then it will rain tomorrow with probability .58.
• If it rained yesterday but not today, then it will rain tomorrow with probability .29.
• If it rained today but not yesterday, then it will rain tomorrow with probability .47.
• If it did not rain yesterday or today, then it will rain tomorrow with probability .31.

Even though the weather depends on the last two days in this case, we can create a Markov chain model using the states

1 it rained yesterday and today

2 it rained yesterday but not today

3 it rained today but not yesterday

4 it did not rain yesterday or today

So, for example, the probability of a transition from state 1 to state 1 is .58, and the transition from state 1 to state 3 is 0.
a. Complete the creation of the transition matrix for this Markov chain.
b. If it rains on Tuesday and is clear on Wednesday, what is the probability of no rain on the next weekend?