- 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?

• P(A wins) = P(Die 1 lands red) * P(Die 2 lands red) + P(Die 1 lands blue) * P(Die 2 lands blue)
  
  So if r represents the number of red faces on the 2nd die and we want P(A wins) to be 0.50 (50%), then
  0.50 = 4/6 * r/6 + 2/6 * (6-r)/6
  0.50 = 4r/36 + (12-2r)/36
  18/36 = (12-2r)/36
  18/36 = 12/36 - 2r/36
  6/36 = 2r/36
  6 = 2r
  3 = r
• 13 years agoHelpfull: Yes(5) No(2)