There are three ants on different vertices of a triangle What is the probability of collision (between any two or all of them) if they start walking on the sides of the triangle?

Similarly find the probability of collision with "n" ants on an "n" vertex polygon

• Every Ant can move in 2 possible directions , backward and forward ( B or F ) , so the whole sample space consists of 8 choices, out of which 2 , namely BBB and FFF are no collision choices.
  
  So probability of not colliding is 2 /8 = 1/4 = 0.25
  
  Sample space:
  
  F F B
  
  F F F
  
  F B B
  
  F B F
  
  B F B
  
  B F F
  
  B B B
  
  B B F
  
  So probability of colliding is = 1 - 0.25 = 0.75
• 11 years agoHelpfull: Yes(67) No(1)
• In general case(for 'a' ants on 'a' vertices):
  
  total outcomes = 2 x 2 x 2 x ...a = 2ª
  
  no collision = 2
  
  probability of no collision = 2/2ª
  
  So, probability of collision = 1 - 2/2ª
  
• 11 years agoHelpfull: Yes(22) No(0)
• total no of ways of walking=8,
  no of ways they won't collide=2
  so probability = (8-2)/8=3/4
  
  
  general solution=1-2^(1-n)
• 11 years agoHelpfull: Yes(3) No(1)
• 2/3
  (n+1)/2n
  
• 11 years agoHelpfull: Yes(1) No(7)
• @anshu is it sme kinda formula?
  
• 11 years agoHelpfull: Yes(0) No(4)
• ans is .75
  
• 11 years agoHelpfull: Yes(0) No(0)