Two cubes have their face painted as either red or blue color. 1st cube has 5

Discussion Forum : Probability I

Question -

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

Options:

A . 6

B . 4

C . 3

D . 2

Answer: Option C
:
C

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

P(RR or BB)= $\frac{5}{6} \times \frac{x}{6} + \frac{1}{6} \times \frac{(6 - x)}{6} = \frac{1}{2}$

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

4x+6=18

x=3

Hence number of red faces is 3.

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