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# Consider a game of ladder climbing There are 5 levels in the game level 1 is the lowest (bottom) and level 5 is the highest top A player starts at the bottom Each time a fair coin is tossed

Consider a game of “ladder climbing.” There are 5 levels in the game, level 1 is the lowest (bottom) and level 5 is the highest (top). A player starts at the bottom. Each time, a fair coin is tossed. If it turns up heads, the player moves up one rung. If tails, the player moves down to the very bottom. Once at the top level, the player moves to the very bottom if a tail turns up, and stays at the top if head turns up. Define a Markov chain {Xn, n = 1, 2, 3, · · ·} as the level of the player at the nth time step.
Suppose the probability of falling to the ground is 1 10 if one is on the level 1, 2 10 if one is on the level 2, 3 10 on the level 3, 4 10 on the level 4, and 5 10 on the level 5. What is the long term probability that the person on the ladder falls to the ground? (Hint: You need to use a conditional probability.)

Apr 02 2020 View more View Less Subscribe To Get Solution