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 $\frac{1}{2} .$ The number of red faces on the second cube, is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $3$
Given two cubes have their faces as red or blue, first cube has five faces as red and one as blue.
$\Rightarrow$ Probability of first cube to have its face as red $= \frac{5}{6}$
and Probability of first cube to have its face as blue $= \frac{1}{6}$

Let the second cube has $x$ faces as red.
$\Rightarrow$ Probability of second cube to have its face as red $= \frac{x}{6}$
and Probability of second cube to have its face as blue $= 1 - \frac{x}{6}$

Given, probability that the two top faces show the same colour,
$P (R R or B B) = \frac{1}{2}$
$\Rightarrow \frac{5}{6} \cdot \frac{x}{6} + \frac{1}{6} \cdot \frac{6 - x}{6} = \frac{1}{2}$
$\Rightarrow 5 x + 6 - x = 18$
$\Rightarrow 4 x = 12$
$\Rightarrow x = 3$

Suggest Corrections

Similar questions

Q. 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.

Two cubes have their face painted as either red or blue color. $1 s t$ 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 $2 n d$ cube.

Q. A cube painted red on all sides is cut into 125 equal small cubes. A small cube when picked up is found to show red colour on one side of its face. The probability that two more faces also show red colour is

Q. A cube is painted red on two adjacent faces and on one opposite face, yellow on two opposite faces and green on the remaining face. It is then cut into

64

equal cubes. How many cubes have only one coloured face as red?

Q. Two faces each of a cube of side 6 cm have been painted blue, red and yellow. If it is cut into cubes of side 1 cm each, then how many small cubes will have ONLY ONE side painted either blue or red?

Join BYJU'S Learning Program

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 12. The number of red faces on the second cube, is

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 $\frac{1}{2} .$ The number of red faces on the second cube, is