Ram and Shyam have a cube each. Ram paints four faces of cube with red color and rest with blue color. Ram asks Shyam to paint his cube as well with some sides red and some side blue. They now start rolling the cubes simultaneously. After doing this for very long Ram observes that probability of both cubes coming up with same color is 1/3. How many faces of his cube did Shyam paint red ?  Choose one.
A) 0  B) 2  C) 3  D) 4  E) 5
Explanation :   Let Shyam paints n faces of the cube red. So faces painted blue = (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 =&gt; n = 0   So Shyam hasn't painted any of the face with red color.   0nswer : 0
<result>A</result>
Ram and Shyam have a cube each. Ram paints four faces of cube with red color and rest with blue color. Ram asks Shyam to paint his cube as well with some sides red and some side blue. They now start rolling the cubes simultaneously. After doing this for very long Ram observes that probability of both cubes coming up with same color is 1/3. How many faces of his cube did Shyam paint red ?