- 14 Jun '06 19:23Suppose we have a triangle with vertices A,B,C and a slug that travels around its perimeter. Whenever the slug reaches a vertex, it has a 1/2 chance of moving toward each of the remaining two vertices.

Suppose the slug starts out at vertex A. After the slug has moved 10 triangle side lengths, what is the probability that the slug will find himself back at point A? After moving 20 side lengths, what is the probability that he will be at point C? - 14 Jun '06 22:14

I agree with your first answer -- well done.*Originally posted by aging blitzer***after 10 lengths I make it 171/512**

after 20 lengths I make it 174763/524288

For the second question, I got something very slightly different. I get that your answer would be the probability for the slug to end up at A after 20 moves -- not C. I could have made a mistake, but notice that your second answer is greater than 1/3, which at first glance should be a strike against its being correct. - 15 Jun '06 07:26 / 1 editas you surmised, I didn't read it right.

to be at C after 20

349525/1048576

edit:

either 1 or 2 points will have a greater than 1/3 probability.

after an odd number of moves A < 1/3, B > 1/3, C > 1/3

after an even number of moves A > 1/3, B < 1/3, C < 1/3

so, yes, after 20 the probability of C should be < 1/3 - 15 Jun '06 19:34

Let An, Bn, and Cn denote the chance of being in A, B and C respectively after n moves.*Originally posted by aging blitzer***as you surmised, I didn't read it right.**

to be at C after 20

349525/1048576

edit:

either 1 or 2 points will have a greater than 1/3 probability.

after an odd number of moves A < 1/3, B > 1/3, C > 1/3

after an even number of moves A > 1/3, B < 1/3, C < 1/3

so, yes, after 20 the probability of C should be < 1/3

A0 = 1, B0 = C0 = 0

An = B(n-1)

Bn = 1/2 * (1 - An)

Cn = Bn

I currently have no program to check the answers given - 15 Jun '06 20:49

Well done.*Originally posted by aging blitzer***as you surmised, I didn't read it right.**

to be at C after 20

349525/1048576

edit:

either 1 or 2 points will have a greater than 1/3 probability.

after an odd number of moves A < 1/3, B > 1/3, C > 1/3

after an even number of moves A > 1/3, B < 1/3, C < 1/3

so, yes, after 20 the probability of C should be < 1/3