Ram and Shyam have a cube each. Ram paints 4 faces of cube with red colour and rest with blue colour. Ram asks Shyam to paint his cube as well with some sides red and some sides blue. They now start rolling the cubes simultaneously. After doing this for very long Ram observes that probability of both the cubes coming up with same colour is 1/3. How many faces of his cube did shyam paint red.
(a)0
(b)2
(c)3
(d)4

• let x no.of faces painted in red and y no.of faces painted in blue for the shyam's cube, for getting same colour on the both cubes and the color may be red or blue
  red:
  getting red in 1st cube=4/6=2/3
  getting red in 2nd cube= x/(x+y)
  so probability that both comes red= (2/3)*(x/(x+y))............(1)
  similarly for the case of blue
  probability that both coes blue=(1/3)*(y/(x+y))..................(2)
  given that (1)+(2)=1/3
  by solving we get x=0
  
• 11 years agoHelpfull: Yes(39) No(3)
• For ram, prob(blue)=4/6 and prob(red)=2/6.(given)
  So,
  let shyam painted x faces blue and y faces red. so prob(blue)=x/x+y and prob(red)=y/x+y;
  now, as per condition,
  (4/6*x/x+y)+(2/6*y/x+y)=1/3 so ,
  from here x= 0;
  so shyam painted all faces as red=6;
  
• 10 years agoHelpfull: Yes(5) No(5)
• If we paint all the faces of second cube with blue color, we can get the required probability. so no.of faces with red is 0.
• 11 years agoHelpfull: Yes(3) No(4)
• Let Shyam paints n faces of the cube red. So blue faces of Shyam's cube = (6-n)
  
  Probability that both show up same color is: (probability both show red) + (probability both show blue)= 4/6 * n/6 + 2/6 * (6-n)/6
  
  = (2n + 6)/18
  But as given, (2n + 6)/18 = 1/3 => n = 0
  So Shyam hasn't painted any of the face with red color.
  So answer is (a
• 9 years agoHelpfull: Yes(1) No(1)