A string is in the form of a triangle,an insect is sitting on one of the vertex.the probability of taking a path out of the two by the insect is 1/2.what is the number of sample spaces in which insect returns to its original position after travelling 7 paths?

• Ans: 4
  Let string forms ABC triangle.
  insect is sitting on one vertex A
  since, P = n(E)/n(S)
  given, P = 1/2
  Event E = A-B-C-B-C-B-C-A or A-C-B-C-B-C-B-A
  No. of event n(E) = 2
  so, n(S) = 2*2 = 4
• 10 years agoHelpfull: Yes(6) No(0)
• there is only two option after traveling the 7 path
  saple space is - 2
• 10 years agoHelpfull: Yes(3) No(2)
• 42/128....
• 10 years agoHelpfull: Yes(1) No(3)
• ITS NOT ASKING FOR THE PROBABILITY,,ITS ASKIN FOR SAMPLE SPACES OR NO, OF WAYS INSECT CAN RETURN TO ORIGINAL POSITION BY TAKING ONLY 7 PATHS
• 10 years agoHelpfull: Yes(1) No(0)
• it should be 1/3 bcz there 3 three sample spaces, A, B, C
  and desired is A
• 10 years agoHelpfull: Yes(1) No(0)
• please give the explanation @abhishek
• 10 years agoHelpfull: Yes(0) No(0)
• answer is 1/2 because let its at a point A in triangle after traveling 7 paths it will be at B or C point and the prob to go to its original position is 1/2
  
• 10 years agoHelpfull: Yes(0) No(1)
• there are total possible path are 7 and probability to choose them is
  2[1/2*1/2+1/2*1/2*1/2+1/2*1/2*1/2*1/2]+0 = 7/8
• 10 years agoHelpfull: Yes(0) No(0)
• 1 cyclic path ABCA ... 3 paths
  2 return via same path ... 4paths
  
  total 7..now calculate sample space
• 10 years agoHelpfull: Yes(0) No(0)