interesting math question...

[leonsv 10+ year member]

ok so my friend's kid comes to me with this math question that he got from school. I got an answer but want some one to check it.

"A bug starts at one vertex of a cube and moves along the edges of the cube according to the following rule. At each vertex the bug will choose to travel along one of the three edges emanating from the vertex. Each edge has equal probablility of being chosen, and all choices are independent. what is the probability that after seven moves the bug will have visited every vertex once?"

after some work that i really don't feel like typing (a lot of capital letters, fractions, and exponents) i got that the probability was 2/243

can some one check this?

thanks

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[bigwheel15 10+ year member]

The answer is 5.

 

[leonsv 10+ year member]

The answer is 5.

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[LinxuS 10+ year member]

Isn't it just (1/3) ^ 7 ?

1/2187

Independent means that the first does not affect the next..

So 1/3 for the first right path

1/3 for the next

1/3 for the next

and so on..

(1/3) x (1/3) x (1/3) x (1/3) x (1/3) x (1/3) x (1/3) = (1/2187) =~ .000457

 

[stuntman]

i agree with linxus its 1/3^7

 

[faulkton 5,000+ posts]

oxymoron

 

[jmanpc 5,000+ posts]

the square root of my nuts is skeet.