Show transcribed image text 1. (10 points) (Without Python) A gambler starts with $15 and plays a game where the chance of winning each round is 49%. The gambler either wins or loses $1 on each round. The game stops when the gambler reaches 850 or goes bust. Let (Xn)n00 be a SDTMC where Xn represents the gambler's winnings at round n. (a) Find the transition probabilities for the Markov chain (Xn/n=0. (b) Calculate the probability that the gambler will be ruined. That is, what is the probability that the gambler ends up with S0. (If you'd like, you may show all of your work setting up a system of equations and then use Python to solve the system.) (c) Calculate the probability that the gambler will reach 850. (If you'd like, you may show all of your work setting up a system of equations and then use Python to solve the system.)
1. (10 points) (Without Python) A gambler starts with $15 and plays a game where the chance of winning each round is 49%. The gambler either wins or loses $1 on each round. The game stops when the gambler reaches 850 or goes bust. Let (Xn)n00 be a SDTMC where Xn represents the gambler's winnings at round n. (a) Find the transition probabilities for the Markov chain (Xn/n=0. (b) Calculate the probability that the gambler will be ruined. That is, what is the probability that the gambler ends up with S0. (If you'd like, you may show all of your work setting up a system of equations and then use Python to solve the system.) (c) Calculate the probability that the gambler will reach 850. (If you'd like, you may show all of your work setting up a system of equations and then use Python to solve the system.)
