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:

3 red sides and 3 blue sides

Step-by-step explanation:

Given that , the dice has 5 number of red sides

                                 and 1 number of blue sides

Let the second dice has x number of red sides

                                 and y number of blue sides.

Favourable Cases for first person to win  is that same color should appear on both the dies = 5x (for both showing red) + y (for both showing blue).

Favourable Cases for second person to win  is that different color should appear on both the dies = 5y (for dice 1 showing red and dice 2 showing blue) + x (for dice 1 showing blue and dice 2 showing red).

But , it is given that Odds of both the persons winning are equal.

Hence 5x + y = 5y +x

=> x =y

Also, we know x + y = 6(total number of faces on a dice)

Thus we get , x = y = 3.