A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
option
a) 3 red and 3 blue faces
b) 2 red and remaining blue
c) 6 red and 0 blue
d) 4 red and remaining blue

• ANS is 3 red and 3 blue faces
  Let 2 dice contains x no of red faces and y no of blue faces
  probability of winning A=(4/6)*(x/6)+(2/6)*(y/6)
  probability of winning B=(2/6)*(x/6)+(4/6)*(y/6)
  both probabilities are equal according to the given condition
  therfore 4x+2y=2x+4y
  x=y
  hence x=3 and y=3
• 13 years agoHelpfull: Yes(151) No(6)
• here, Probability of Winning = Probability of losing = 1/2
  
  So, Probability of both red is 4/6 * x/6 [ where x is the number of red faces on the other die ]
  
  Probability of both blue is 2/6 * (6-x)/6
  
  so
  Probability of same color = PRobability of both red OR Probability of both blue
  
  = 4/6 * x/6 + 2/6 * (6-x)/6 = 1/2
  
  4x/36 + (12-2x)/36 = 1/2
  
  12+2x=18
  
  2x = 6
  
  x=3
  
  So red=3 and blue=3
• 13 years agoHelpfull: Yes(52) No(2)
• Answer: a
  Chances of winning of A = 4/6 * 3/6 + 2/6 * 3/6 = 18/36
  Chances of winning of B = 1 - 18/36 = 18/36
• 13 years agoHelpfull: Yes(12) No(5)
• ans is a..
  choosing red from 2 boxes is 2/3 and 1/2.
  choosing blue from 2 boxes is 1/3 and 1/2.
  
  for A to win,same colors occur.
  (2/3)*(1/2)+(1/3)*(1/2)=(1/2)
  
  for B to win,different colors occur.
  (2/3)*(1/2)+(1/3)*(1/2)=(1/2)
• 13 years agoHelpfull: Yes(5) No(1)
• to get equal chance of winning..the dice must be unbiased....so the second die must contain 4 red and 2 blue faces...so the answer is D
• 13 years agoHelpfull: Yes(4) No(19)
• 2 red and remaining blue
• 13 years agoHelpfull: Yes(2) No(32)
• b) 2 red and remaining blue.
• 13 years agoHelpfull: Yes(2) No(16)
• can anyone plzz tell which is d correct answer..
• 11 years agoHelpfull: Yes(2) No(0)
• For both of them to have an equal chance of winning,
  The probability that a single color pops up on the two dice should be half
  So, Probability (dice 1 is red AND dice 2 is red) + Probability (dice 1 is blue AND dice 2 is blue) = 1/2
  Let the other dice have x red faces
  So, it will have 6-x blue faces
  So,
  (4/6)*(x/6) + (2/6)*(6-x)/6 = 1/2
  So, x = 3, y=3
• 10 years agoHelpfull: Yes(1) No(0)
• 4 red 4 blue. as there are 4 red 2 blue sides in dice 1.
• 13 years agoHelpfull: Yes(0) No(9)