P2. Monte Carlo. You have one fair die (each number 1-6 is equally probable). How many throws would you expect to roll two sixes in a row? Provide a python code to solve this. Hint: The answer is 42 . This problem can be solved mathematically or with code. Mathematically, this problem is solved using a Markov Chain. A Markov Chain is when past and future states are equally independent. Below is the transition graph for this scenario: " S " denotes the starting state, " 6 " denotes when a 6 is rolled and " 66 " represents when two 6's are rolled in a row. If we start on the left, we can see that there 5/6 probability of rolling something other than 6 , so you would just start at the beginning. To get to the " 6 " state, you have a 1/6 probability. From there, you have a 5/6 probability to not roll a 6 and go back to the beginning, or you have a 1/6 probability to roll a 6 again and end the streak. The number of rolls, X, can be represented by the following formula: X=(1p)(1+X)+p(1p)(2+X)+p2(2) This formula has all of the above states accounted for and will give you a final answer of 42. A Monte Carlo python code will give you close to this number given a large enough sample size. Please provide this information in a .py or jupyter-notebook file. (It can be the same jupyter-notebook file as problem 1.)