Question

Two cubes have their faces painted either red or blue. The first cube has five red faces and one blue face. When the two cubes are rolled simultaneously, the probability that the two top faces show the same colour is 1/2. Number of red faces on the second cube, is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Given, Two cubes have their faces as red or blue.First cube have 5 faces as red and 1 face as blue

$\Rightarrow$ Probability of first cube to have its face as red$=\frac{5}{6}$

$\Rightarrow$ Probability of first cube to have its face as blue$=\frac{1}{6}$

Let second cube have $x$ faces as red.

$\Rightarrow$ Probability of second cube to have its face as red$=\frac{x}{6}$

$\Rightarrow$ Probability of second cube to have its face as blue$=(1-\frac{x}{6})$

$\therefore$ The probability that cubes show same color when thrown$=\left(ProbabilityshowingbothasRed\right)+\left(ProbabilityshowingbothasBlue\right)$

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

$\Rightarrow 5x-x+6=18$

$\Rightarrow x=3$

The second cube should have $3$ red faces to satisfy above relation.