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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 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
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19 Mar 2007, 06:55
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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.
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.
19 Mar 2007, 06:57
Kudos
Bookmarks
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
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
