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A ladybug is walking at random on a hexagon. She starts at vertex A.Every minute, she moves to one of the two vertices (chosen at random) adjacent to the one she's currently on. What is the probability that, after 10 minutes, she is back at A?

 May 31, 2021

Best Answer 

 #1
avatar+2207 
+1

There are 3 cases to work out.

RRRRRRRRLL (right and left) in some combination and LLLLLLLLRR (left and right) in and LLLLLRRRRR. 

2*10C2 + 10C5

2*45 + 252 = 342

 

I hope that's right. :)

 

=^._.^=

 

Edit:

It asked for probability, not number of ways, I also missed one of the cases from before. 

2^10 is that total number of ways. 

342/1024  = 171/512

 

=^._.^=

 May 31, 2021
edited by catmg  May 31, 2021
 #1
avatar+2207 
+1
Best Answer

There are 3 cases to work out.

RRRRRRRRLL (right and left) in some combination and LLLLLLLLRR (left and right) in and LLLLLRRRRR. 

2*10C2 + 10C5

2*45 + 252 = 342

 

I hope that's right. :)

 

=^._.^=

 

Edit:

It asked for probability, not number of ways, I also missed one of the cases from before. 

2^10 is that total number of ways. 

342/1024  = 171/512

 

=^._.^=

catmg May 31, 2021
edited by catmg  May 31, 2021
 #2
avatar+114525 
+1

That is impressive logic catmg.       laugh laugh cool

 

I think you have it!

 May 31, 2021
 #3
avatar+2207 
+1

Thank you. :))

 

=^._.^=

catmg  Jun 1, 2021

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