# Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picking a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collides?<

**Updated:**March 7, 2021 —

**Training Time:**1 Minute

Overseen by: Archangel Macsika

**Topic:** Data Science.

**Difficulty:** Easy.

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**Objective:** Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picking a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collides?<

**Short Answer: 1/4**.

### Full Solution

First, for the ants to avoid a collision, we will assume that they must all move in one direction, which can be either clockwise or anti-clockwise.

If they do not move in one direction, there will definitely be a collision.

However, each ant independently has the option to either move in a clockwise or anti-clockwise direction.

This means that there is a one in two chance that an ant decides to pick a particular direction.

Therefore, the probability of no collision occurring can be illustrated as:

=(Probability of all ants going in a clockwise direction) + (Probability of all ants going in an anti-clockwise direction)

= (0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) = 0.25

= 1/4