A and B plays a game of dice between them. The consist of colors on their faces ( instead of numbers). When the dices are thrown, A wins if both show the same color. Otherwise B wins. One die has 4 re 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?
a)3 red and 3 blue b) 2 red and remaining blue c) 6 red and 2 blue d) 4 red and 2 blue

• It's A. if we take 3 red and 4 red then we have combination 12 and if we take 3 blue and 2 blue then we have 6 combinations of similar colour.so we have 12+6=18 similar colour combinations.we total have 6*6=36 combinations.so we have 18 different colour combinations.
• 10 years agoHelpfull: Yes(20) No(1)
• Ans is A.
  probability of win of a = probability of win of b.let x is red and y is blue.
  ((1/4)*(1/x))+((1/2)*(1/y))=((1/4)*(1/y))+((1/2)*(1/x))on comparing x=y i.e. x=y=3
• 10 years agoHelpfull: Yes(17) No(0)
• Second dice has n red faces and (6-n) blue faces
  
  For A and B to have an equal chance of winning probability of A winning = 0.5
  Probability of A winning = [1/6 * (n/6)] + [5/6 * (6-n)/6] = 0.5
  n/36 + (30-5n)/36 = 18/36
  n + 30 - 5n = 18
  30 - 4n = 18
  4n = 12
  n = 3
  
  The second dice must have 3 red faces and 3 blue faces
• 10 years agoHelpfull: Yes(11) No(0)
• b. 2 red and 4 blue
• 10 years agoHelpfull: Yes(5) No(16)
• ans:b because, the probability to get same color from both dice is i.e,consider red from both dice 4*2 next blue i.e, 2*4 total 4*2+2*4=16 combinations.
  similarly for different colors it will be 4red*2 blue on one dice and 2 red*4 blue on the other dice total 4*2+2*4=16. both probabilities were same so, they get same chances to win.
• 10 years agoHelpfull: Yes(2) No(1)
• admin can you explain with solution
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• hai admin can u explain this in the perfect way
  
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• here the chances of winning are same. so, the probability must be 1/2 as there are only 2 persons. hence, cross check the options where you can get a probability of 1/2. take option a, thn
  4 red and 3 red i.e; 4*3=12 combinations. similarly, for blue 2*3=6. total combinations=12+6=18. so, probability=18/36=1/2.
  No other option will satisfy this..
• 10 years agoHelpfull: Yes(1) No(0)
• let the other dice has x red and y blue faces.no of posible combination of winning=RR or BB means same colors on both dices.so probablity of winning=(4/6)*(x/x+y)+(2/6)*(Y/x+y)
  similarly combination of losing are RB or BR.
  PROB of losing=(4/6)*(y/x+y)+(2/6)*(x/x+y)
  since both prob is equal
  solving we get X=y
  so a is correct
  
• 10 years agoHelpfull: Yes(1) No(0)
• hi nithish can u explain it...??
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• 3red and 3 blue as there are equal chances of wnning
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• The probability of winning for A is 18/36
  No of total outcomes 36
  no of favourable outcomes for A are 4x*2y where x is no of red faces in 2nd die and y is no of blue faces in 2nd die
  probability of A winning=18/36=(4x*2y)/36
  solving above eqtn we get x=3 and y=3
  Ans:- red=3 blue=3
  
• 10 years agoHelpfull: Yes(0) No(0)