Puzzle:
Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
Puzzle Solution:
So let’s think this through. The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will definitely be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one in two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.
P(No collision) = P(All ants go in a clockwise direction) + P( All ants go in an anti-clockwise direction) = 0.5 * 0.5 * 0.5 + 0.5 * 0.5 * 0.5 = 0.25
A simple way to solve.
P(#collision)= # of way when there is no collision/ total number of way ants can move
= 2/2^3
= 1/4
there is only 2 way when there is no collision when all 3 ants move clockwise or anticlock wise
and there are 3 ants and each can move in 2 direction so there will be 2^3 way they can move.
nice
nice explanations both.
Each ant has 2 possibilities of moving in a direction.. clockwise or anti-clockwise. Now as there are 3 ants .. we have 8 total possibilities of the ants moving in a direction.
Now out of 8 we can have only 2 possibilities where they will not collide.
i.e if all the ants travel clockwise or all the ants travel anti-clockwise.
so the probability is 2/8 = 1/4 = 0.25
thanku for the info.
simple and nice explanation thanx!!
Let the 3 ants x, y, z
anticlockwise- A & clockwise C
{xA,yA,zA}
{xA,yA,zC}
{xA,yC,zC}
{xC,yC,zC}
{xC,yA,zA}
{xC,yC,zA}
{xC,yA,zC}
{xA,yC,zA}
Here in 8 cases only in 2 cases there will be no collision when all the ants will travel in same direction either clockwise or anticlockwise.
i.e
{xA,yA,zA}
{xC,yC,zC}
so 2/8= 1/4 = 0.25
nice
Best explanation. I was confused which are those 8 moves. Thanks for listing those 8 available options.
Thanks for detailed description!
Three Ants:
0–>clockwise
1–>Anticlockwise
All combinations will be :
A B C
0 0 0 [No collision]
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1 [No collision]
Probability = 2/8=0.25
Question lacks a lot of useful info. Speed of ants should be same. Also, they should start moving simultanesouly, not randomly.
what is probability of colliding???
6/8
it is assumed that ant travel with same speed
Nice explanation
Nice collections
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