Three cars A, B and C are participating in a race.A is twice as likely as B to win and B is thrice as likely as C to win. What is the probability that B will win, if only one of them can win the race?

• p(A)=2*p(B)
  P(B)=3*p(c)
  P(A) +P(B)+P(C) =1
  2 * P(B) + P(B)+P(B)/3 =1
  10*p(B) /3=1
  P(B)=3/10
• 11 years agoHelpfull: Yes(58) No(0)
• Let the probability of A to win is 'x'. Now B to win is A/2 i.e x/2.
  Now C to win is B/3 i.e x/6.
  So inorder to B to win the probality is (x/2)/(x+x/2+x/6)=3/10.
• 11 years agoHelpfull: Yes(28) No(4)
• let B's chance is x
  then A's chance is 2x
  C's chance is (1/3)x.....(as B is thrice of the c)
  A:B:C=2x:x:(1/3)x
  =6:3:1
  so the probability of B is =3/10
• 10 years agoHelpfull: Yes(4) No(0)
• let B's chance is x
  then A's chance is 2x
  C's chance is (1/3)x.
  A:B:C=2x:x:(1/3)x
  =6:3:1
  winning probablity
  so p(A)=6/10
  p(B)=3/10
  p(C)=1/10
  then the probablity that only B can win=(winning probablity of B)*(losing probablity of A)*(losing probablity of C)
  =3/10*(1-6/10)*(1-1/10)
  =.108
• 10 years agoHelpfull: Yes(2) No(0)
• ans is 27/250
• 11 years agoHelpfull: Yes(0) No(7)
• p(b)=3/10
  but only probability of b is 27/250
• 11 years agoHelpfull: Yes(0) No(7)
• Answer is 3/10
• 3 years agoHelpfull: Yes(0) No(0)
• A:B=2:1
  B:C=3:1
  A;B:C=6:3:1
  B=3/10
• 2 years agoHelpfull: Yes(0) No(0)