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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 9E
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Question

Consider the 3-square random process below. We found the state
transition diagram and the transition probability matrix. Modify the
diagram and matrix so that when the puzzle is solved, it no longer leaves the solved state. It just
stays there. Just submit the matrix 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
E≥EF
P = PH,
1
12
8
q = Pv,
x 3
2 1
PH
Pv
3
6
p+q=1
x 2
1 3
21
4
3
р
q
2
р
q
q
р
р
q
q
Р
р
q
î
3
P =
q
р
р
q
q
р
2
р
q
q
р
12
q
р
Transcribed Image Text: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 E≥EF P = PH, 1 12 8 q = Pv, x 3 2 1 PH Pv 3 6 p+q=1 x 2 1 3 21 4 3 р q 2 р q q р р q q Р р q î 3 P = q р р q q р 2 р q q р 12 q р
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