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Consider a random walk on an infinite two-dimensional triangular lattice, a part of which is shown in the figure below.
If the probabilities of moving to any of the nearest neighbour sites are equal. What is the probability that the walker returns to the starting position at the end of exactly three steps?
  • a)
    1/36
  • b)
    1/216
  • c)
    1/18
  • d)
    1/108
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a random walk on an infinite two-dimensional triangular latti...
A person can take 1st step in any direction independently
Suppose he moves to A
Now to return to O ( initial point) in 2 steps he can move in 2 directions. Either B or f
Thus probability he will move to either B or F will be = 2/6
Suppose he moves to B
Now to return back to O
he has only 1 option
⇒ to move in BO
Probability he will move in BO direction  = 1/6
Total probability he will return
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Consider a random walk on an infinite two-dimensional triangular lattice, a part of which is shown in the figure below.If the probabilities of moving to any of the nearest neighbour sites are equal. What is the probability that the walker returns to the starting position at the end of exactly three steps?a)1/36b)1/216c)1/18d)1/108Correct answer is option 'C'. Can you explain this answer?
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