You and 3 others (B, C, D) sit in a circle. You start with a ball. Every second, the person with the ball can either:
- Pass it left, - Pass it right, or - Keep it (ending the game), All with equal probability (1/3 each). What is the probability that you (person A) end the game by keeping the ball?
Solution:
""" Markov Chain graph representing the ball-passing game: - Each node (A, B, C, D) represents a person. - Arrows show the possible transitions each second. - Edge labels indicate the transition probabilities (each 1/3). - A self-loop means the person keeps the ball and ends the game."""import networkx as nx import matplotlib.pyplot as plt# Create directed graph G = nx.DiGraph()# Define states states = ['A', 'B', 'C', 'D'] transitions = { 'A': [('A', 1/3), ('B', 1/3), ('C', 1/3)], 'B': [('A', 1/3), ('B', 1/3), ('D', 1/3)], 'C': [('A', 1/3), ('C', 1/3), ('D', 1/3)], 'D': [('B', 1/3), ('C', 1/3), ('D', 1/3)], }# Add edges with weights for from_state, to_states in transitions.items(): for to_state, prob in to_states: G.add_edge(from_state, to_state, weight=prob)# Set layout pos =…
