The breakdown of machines and structures are often modeled using Markov chains. One example of this is the deterioration of bridges. Imagine a new rope bridge in the Andes mountains held up by 3 jut ropes. Every time a person crosses the bridge, there is a chance that one of the ropes will break. Let pn be be the probability that one of the ropes breaks when there aren ropes, and assume that two ropes never break at once. For our purposes, pn=1/200n

1. Draw of this Markov chain. Label all nodes with their corresponding state, and all edges with their transition probability. Discuss any uncertainties in the model structure and parameterization.
2. Construct a transition matrix for changes in the bridge's state every time a person crosses the bridge.
3. If the Markov chain begins when the bridge is first built, what is the initial condition?
4. What is the probability that the bridge will have collapsed by the time 1000 people have crossed it? Hit: Use python to perform this calculation. Be sure to explain your answer.)