The probability is 25% because there are 3 ants all with
two possible paths and 8 total possible outcomes. But
there are two possible outcomes that the ants don't
collide. Either they move one way or the other. 2/8 = 25%.
Each ant can move in 2 directions. Lets say direction are
Left (L) and Right (R). Solution if all ants move either
towards L or R. For L (1/2 * 1/2 * 1/2) = 1/8. Same for R =
1/8. Total for L and R = 1/8 + 1/8 = 1/4.
actually we have to take care that no 2 ants should
collide....therefore, that is only possible if 1st follows
the second and second follows the third and third follows
the first..........plus it can be either clockwise or
anticlockwise....hence 2 ways out of 8 ways.....ans is
Actually we can say with absolute certainty that two of the
ants will move in the same direction. One of them may not.
It is a trick question. There is a 50/50 chance that one of
the ants may not move in the same direction as the other two.
So the answer is 50%.
There are four dogs, each at the counter of a large square.
Each of the dogs begins chasing the dog clockwise from it.
All of the dogs run at the same speed. All continously
adjust their direction so that they are always heading
straight towards their clockwise neighbor. How long does it
take for the dogs to catch each other? Where does this
happen? (Hint: Dog's are moving in a symmetrical fashion,
not along the edges of the square).