Probability Question

Question

Donald, Douglas, and Duane are playing a dice game.  A pair of dice is tossed and the winner is determined by the sum on the dice.  If the sum is 2, 3, 11, or 12, Doland wins.  If the sum is 4, 5, 9, or 10, Douglas wins.  if the sum is 6, 7, or 8, Duane wins.  Who is most likely to win this game?  Explain why.

Answer 1

There are 36 potential rolls (6 * 6).  So now count the possibilities of each number:

 

2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/26
12: 1/36

 

Doland: P(2,3,11,12) = (1+2+2+1)/36 = 6/36 

Douglas: P(4,5,9,10) = (3+4+4+3)/36 = 14/36

 

So Douglas is 14/6 (which reduces to 7/3) times more likely to win the game than Doland.