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An ant moves on the following lattice, beginning at the dot labeled A. Each minute he moves to one of the dots neighboring the dot he was at, choosing from among its neighbors at random. What is the probability that after 5 minutes he is at the dot labeled B ?

 

 Feb 17, 2019
 #1
avatar+23321 
+4

An ant moves on the following lattice, beginning at the dot labeled A. 

Each minute he moves to one of the dots neighboring the dot he was at, choosing from among its neighbors at random.

What is the probability that after 5 minutes he is at the dot labeled B ?

 

see: https://web2.0calc.com/questions/probability-help_9#r2

 

laugh

 Feb 18, 2019
 #2
avatar+28198 
+5

An alternative to heureka's method is to notice that after 5 moves the ant can only end up at one of the four dots directly connected to A.  There are four of them, and nothing to prefer one over the other, hence the probability of ending up at B is 1/4 or 25%.

 Feb 18, 2019
 #3
avatar+105654 
+1

That is a really helpful observation Alan. It makes the problem trivial. I'm impressed  :)

Melody  Feb 18, 2019
 #4
avatar+1808 
+2

Alan’s observation not only demonstrates a logical solution for this question, but also demonstrates how to think outside the box or the grid. When a process works, it’s very human to stay in our “space” and not consider ideas outside that space. Education, training, and experience all contribute to our thinking processes, and create predetermine modes of operational thought.

 

When we use our minds, instead of our machines, we see parts of our world become as new.smiley

GingerAle  Feb 19, 2019

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