Question

Two people are playing with a pair of dies. Instead of numbers, the dies have different colors on their sides. The first person wins if the same color appears on both the dies and the second person wins if the colors are different. The odds of their winning are equal. If the first dice has 5 red sides and 1 blue side, find the color(s) on the second one?

Answer 1

Answer : $\bold{3 \: Red \: and \: 3 \: Blue}$



Explanation -

Number of sides a dice has = 6

First dice has 5 Red sides and 1 blue side

Probability of red side = 5/6

Probability of blue side = 1/6

Let the x sides are red and blue

Probability to get both colours are same -

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


$\dfrac{5x}{36} + \dfrac{6 - x}{36} = \dfrac{1}{2}$


$\dfrac{5x + 6 - x}{36} = \dfrac{1}{2}$


$2(5x + 6 - x) = 36$


$10x + 12 - 2x = 36$


$8x + 12 = 36$


$8x = 36 - 12$


$x = \dfrac{24}{8} = 3$


Hence :

Answer : $\bold{3 \: Red \: and \: 3 \: Blue}$