probability

Question

Four players, Alice, benny, Carl, and darra, are going to play a game. Alice will begin. she will roll three fair dice. if the three numbers showing up on top have a sum of 13, then Alice wins the game. if they have any other than 13, then the dice go to benny. If benny then rolls the sum of 7, he wins the game. if he does not roll 7, then the dice go to Carl. if Carl then rolls the sum of 10, he wins the game. if Carl does not roll 10. then Darra wins. find the probability of darra winning. Round your answer to the nearest 0.01%

Answer 1

Each roll of the dice is independent of any prior roll. In a three dice game, there are 216 possible rolls ( 6 x 6 x 6).

 

So, when Alice rolls the dice, her chance of rolling a sum of 13 is based on the fact that in a three dice game, there are 21 ways to roll a total of 13.  So, 21/216 = 9.72%

 

After she rolls the dice, Benny will roll them, and there are 15 ways to roll a sum of 7. So, 15/216 = 6.94%.

 

After Benny, Carl has to roll a sum of 10. There are 27 ways to roll a sum of 10. So, 27/216 = 12.50%

 

All of the other possibilities will mean that Darra will win. So, (216 - 27 - 21 - 15) / 216 = 70.83%

 

Lucky Darra!