Three players A, B,C are in a race.A is twice as likely to win as B and B is twice as likely to win as C. Then what is the probability that B wins?

• Probability that B wins = 2/7
  
  Let,
  A wins, p(A) = 2* p(B)
  B wins, p(B) = 2* p(C)
  c wins, p(C) = p(c)
  
  Assume that C wins 1 times means,
  p(C) = 1
  p(B) = 2*1 = 2
  p(A) = 2*2 = 4
  
  Total, p(S) = p(a)+p(b)+p(c)
  p(S) = 4 + 2+ 1
  p(S) = 7
  
  Probability of B wins, = p(B)/ p(S) = 2/7
• 12 years agoHelpfull: Yes(4) No(0)
• Let the probability of C = X.
  Then, the probability of B will be 2X and the probability of A will be 4X.
  The probability of wining of B = No. of suitable chances/Total chances = 2X/X + 2X + 4X = 2X/7X = 2/7.
• 12 years agoHelpfull: Yes(3) No(0)
• assume, p(C)=x. (0
• 12 years agoHelpfull: Yes(2) No(4)
• probability of B to win is=1/6
  as default probability of each is 1/3
  so A has to win by=1/3
  b=1/3*2=1/6
  c=1/3*2*2=1/12
  
  so ans =1/6
• 12 years agoHelpfull: Yes(0) No(3)
• If C win is= 1
  Then B win =1*2=2
  And A win=2*2=4
  Total sum=7
  Probability of B=2/7
  
• 11 years agoHelpfull: Yes(0) No(0)