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?

• i think 1/3
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• 1/27 because all three have equal probability to move on one of the edges
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• 1/8 as each ant has only 2 ways.
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• each ant has to move either right or each ant has to move to their left. I.E we are left with LLL or RRR out of 8 possible combinations, so ans should be 2/8.
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