Question

Two cubes have their face painted as either red or blue color. $1st$ cube has $5$ faces red and $1$ face blue. The probabilty that both the faces show same color on rolling is $\frac{1}{2}$. How many red faces are present on the $2nd$ cube.

• A. 6
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is C

3

Suppose $x$ faces of cube 2 is red then $6-x$ will be blue.

$P\left(RRorBB\right)=\frac{5}{6}\times \frac{x}{6}+\frac{1}{6}\times \frac{(6-x)}{6}=\frac{1}{2}$

$\frac{5x}{36}+\frac{(6-x)}{36}=\frac{1}{2}$

$4x+6=18$

$x=3$

Hence number of red faces is $3$.