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# My friend claims this problem was offered during his

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My friend claims this problem was offered during his [#permalink]  19 Mar 2007, 05:38
My friend claims this problem was offered during his interview with McKinsey.

There is a triangle, and there is an ant sitting on each vertex. All three ants start running simultaneously. What is the probability that they do not collide if they are running at the same speed?

A) 1/3
B) 2/3
C) 1/2
D) 1/4
E) 1/8

Last edited by stolyar on 19 Mar 2007, 05:59, edited 1 time in total.
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prob [#permalink]  19 Mar 2007, 05:55
Each ant can run in clockwise or in an Anti-clockwise direction. So there can be 8 possible ways in which they can start running. They will not collide only if all 3 run in either clockwise or in an Anti-clockwise direction.
So the required probability is 2/8 = 1/4.

An after thought - this holds good only if the ants run with the same speed otherwise the ants will collide.
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IMO,
Binominal formula will help here. Ants have 2 options; to take on one or the other side of each vertex. The prob being equal-1/2 and i get (1/2+1/2) ^3=1/8+3/8+3/8+1/8. We have the case where all 3 start to go in clockwise direction or all 3 start in counterclockwise direction. Which is 1/8+1/8=1/4
The ans is 1/4
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I would have to say 1/4.

The first ant can start in either direction. The other two ants will have to run in the same direction as the first ant so as not to collide.

P(the second ant runs in same dir as first)*P(the third ant runs in same dir as first)

Since each ant has 2 directions to run in, the Prob. would be:

1/2*1/2 = 1/4.
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Re: prob [#permalink]  19 Mar 2007, 06:01
GMAThopeful wrote:

An after thought - this holds good only if the ants run with the same speed otherwise the ants will collide.

Yes, I also thought that we might need to add the prob. of the speeds, but looking at the answer choices decided that they were talking abt a "head-on" collision.
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Re: Probability :) [#permalink]  08 Apr 2007, 11:01
stolyar wrote:
My friend claims this problem was offered during his interview with McKinsey.

There is a triangle, and there is an ant sitting on each vertex. All three ants start running simultaneously. What is the probability that they do not collide if they are running at the same speed?

A) 1/3
B) 2/3
C) 1/2
D) 1/4
E) 1/8

There are 8 ways (directions) on which each ant can run. Out of these only 2 wont result in collision hence P is 2/8 or 1/4
Re: Probability :)   [#permalink] 08 Apr 2007, 11:01
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