Question: 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?
Answer: 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
To put this in other way :
Any ant can go clockwise or anti clockwise, so they are mutually exclusive events, so total probability = 2 ^ 3 = 8. There are 2 cases - either all ant go clockwise or they go anticlockwise....then there will be no collision, so P(No collision) = 2 / 8 = 0.25
Answer: 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
To put this in other way :
Any ant can go clockwise or anti clockwise, so they are mutually exclusive events, so total probability = 2 ^ 3 = 8. There are 2 cases - either all ant go clockwise or they go anticlockwise....then there will be no collision, so P(No collision) = 2 / 8 = 0.25
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