Question

A game of "Doubles-Doubles" is played with two dice. If a player rolls doubles, the player earns 3 points and gets another roll. If the player rolls doubles again, the player earns 9 more points. How many points should the player lose for not rolling doubles in order to make this a fair game?

Answer 1

27/35 points

Explanation:

The probability of getting one double;

P(getting one double) = 5/36

Probability of getting two doubles is;

P(getting two doubles) = 1/36

Probability of getting no doubles is;

P(getting no doubles) = 1/36

For us to find the Number of points that the player should lose for not rolling doubles, we have;

(12/36) + (5(3 - x)/36) - (5x/6) = 0

(12/36) + (15 - 5x)/36 - 5x/6 = 0

Multiply through by 36 to get;

12 + 15 - 5x - 30x = 0

35x = 27

x = 27/35