Consider the 3-square random process below. We found the statetransition diagram and the transition probability matrix. Modify thediagram and matrix so that when the puzzle is solved, it no longer leaves the solved state. It juststays there. Just submit the matrix P. **Educational Content: Probability of Solving a Scrambled Puzzle****Question:**Starting with a scrambled puzzle, if we proceed by randomly choosing moves, what is the probability that we'll solve the puzzle in N moves?**Puzzle Illustration:**The image shows a simple 2x2 puzzle with tiles numbered 1, 2, and 3.**Explanation of Diagrams:****State Transition Diagram:**The left side of the image shows a state transition map with numbered tiles. Each state represents a different configuration of the tiles:1. **States:** There are 12 distinct states that the puzzle can be in, each represented by a grid with the numbers 1, 2, and 3, and an 'x' indicating the empty space.2. **Transitions:** Arrows between states indicate possible moves. Moves are either horizontal (\(H\)) or vertical (\(V\)).3. **Probabilities:** The transitions have probabilities assigned as either \(p_H\) for horizontal moves or \(p_V\) for vertical moves, with \(p = p_H\) and \(q = p_V\), where \(p + q = 1\).**Probability Matrix (\(\overline{P}\)):**On the right side is a probability matrix \(\overline{P}\) showing the probabilities of moving from one state to another.1. **Matrix Structure:** The matrix is a grid with indices indicating transitions between states.2. **Diagonal Elements:** The diagonal entries primarily contain the probabilities \(p\) and \(q\), indicating the likelihood of moving to an adjacent state horizontally or vertically.3. **Off-Diagonal Elements:** These elements are smaller probabilities reflecting the potential less likely transitions between non-adjacent states.This setup models a Markov process commonly used to analyze random movements within a state space, providing a foundation for calculating the probability of solving the puzzle in a specific number of moves.

Question: Starting with a scrambled puzzle, if we proceed by randomly choosing moves, what is the probability that we'll solve the puzzle in N moves? 11 x 1 32 SU 10 31 2x P = PH, 1 (2₂ PM Je 12. q=Pv, 00 12 3 x 1 x 32 3 1 x 2 x 3 21 PH PH 2 3 6 7 p+q = 1 12 x 3 Pu x 2 13 23 x 1 3 x 21 2x 13 ng J 23 1 x р q 2 Р q q р р q q P Р q 1 3 P = q р р q q р 2 р q q р R q P

Question: Starting with a scrambled puzzle, if we proceed by randomly choosing moves, what is the probability that we'll solve the puzzle in N moves? 11 x 1 32 SU 10 31 2x P = PH, 1 (2₂ PM Je 12. q=Pv, 00 12 3 x 1 x 32 3 1 x 2 x 3 21 PH PH 2 3 6 7 p+q = 1 12 x 3 Pu x 2 13 23 x 1 3 x 21 2x 13 ng J 23 1 x р q 2 Р q q р р q q P Р q 1 3 P = q р р q q р 2 р q q р R q P

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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