3 N ANTS

There are only two possibilities in which collision can be occurred.

• All ants move in counterclockwise direction.
• All ants move in anti-counterclockwise direction.

Since every ant has two choices (pick either of two edges going through the corner on which ant is initially sitting). So for N ants there are total 2N possibilities.

Probability that none of the ants collide = ( 2N  - 2)/ 2N

​           = ( 2N-1   - 1)/ 2N-1

import math

# Non Collide Probability for N ANTS

# N Number of Ants & N > 2

N = 3

# P Probability

P = (math.pow(2,N-1)-1)/math.pow(2,N-1)

print('Probability that none of', N, 'ants collide:', P)

Output:

Probability that none of 3 ants collide: 0.75

If you set N = 4 then output:

Probability that none of 4 ants collide: 0.875

If you set N = 10 then output:

Probability that none of 10 ants collide: 0.998046875