There is a triangle and 3 ants on each vertex of the triangle. The 3 ants start to move randomly along the edges of the triangle. What is the probability that two ants will collide?

• Every ant can move in one of two directions.
  so possible 8 combinations.
  Only two cases are possible when two ants will not collide when all three move in same direction.
  So probability that two ants will collide = 6/8=3/4
• 10 years agoHelpfull: Yes(34) No(5)
• Every ant can move in two directions.
  
  So,for 1st ant there are 2C1=2 possible ways..
  for 2nd ant there are 2C1=2 possible ways..
  for 3rd ant there are 2C1=2 possible ways..
  
  therefore total possible ways = 2*2*2=8 combinations
  
  Now there will be only two cases when two ants will not collide when all three move in same direction
  
  So, there will be 8-2=6 cases when two ants collide
  
  So probability that two ants will collide = 6/8=3/4
• 9 years agoHelpfull: Yes(29) No(0)
• 3 ants each can move in 2 directions =3*2=6
  they will not collide in 2 ways... if all goes in same direction
  p(not collide)=2/6
  p(collide)=1-2/6=2/3
• 9 years agoHelpfull: Yes(7) No(7)
• suppose 3 ants are a,b,c
  now for every ant has only two edge to go through either edge
  so prob of choosing one edge is 1/2
  so prob of meeting ab is (1/2*1/2)=1/4
  likewise for bc = 1/4 and ca=1/4
  so total prob=1/4+1/4+1/4
  ans 3/4
  
  
• 9 years agoHelpfull: Yes(6) No(0)
• let us consider if ands move left or right
  so left =L
  and right =R
  so combinations are
  all move ants in same direction in this case no collision
  RRR
  LLL
  6 cases of collision
  RRL
  RLR
  LRR
  RLL
  LLR
  LRL
  
  TOTAL CASES 8
  P=6/8=3/4
  
• 9 years agoHelpfull: Yes(6) No(0)
• ans = 5/6
  1 case when two ants are not collide when all move in 1 direction
  total cases =6 combination
  left combination =1-1/6=5/6
  
• 10 years agoHelpfull: Yes(3) No(8)
• total (sample space)of 8 ways as first ant 2 ways and sec ant 2 ways and third and 2 ways (2*2*2)=8 ways
  ants don't collide in 2 ways =2/8=1/4
  collide in 1-1/4=3/4
  
• 9 years agoHelpfull: Yes(2) No(2)
• the concept of prerna is correct but a slight mistake, the prob will be 3/8
• 9 years agoHelpfull: Yes(1) No(4)
• only 1 probabilty
  
• 9 years agoHelpfull: Yes(0) No(7)
• 
  Every ant can move in one of two directions.
  so possible 6 combinations.
  Only two cases are possible when two ants will not collide when all three move in same direction.
  So probability that two ants will collide = (1-2/6)=2/3
• 9 years agoHelpfull: Yes(0) No(1)