89 10 11 12 13 14 15 16 17 18 19 20you and two friends (adam and alana) wonly play a game if it is fair for all three of you. the game your friend hasproposed to roll two number cubes (numbered 1-6) and find the sum. if the sum is from 1.4 you get the point. 5-8is adam gets the point, and 9-12 lana gets the point. is this game fair for all three of you? who has the best advantage? turn it inask for question

Well I don't know ! 
Let's take a look and see:

The idea is that there could be more than one way
for a roll of the dice to land with the same number.  

-- If the sum is from 1-4, you get the point.
There are  6  different ways for a roll of the dice to come up 1-4.

-- If the sum is from 5-8, Adam gets the point.
There are  20  different ways for a roll of the dice to come up 5-8.

-- If the sum is 9-12, Lana gets the point.
There are  10  different ways for a roll of the dice to come up 9-12.

-- The game is not fair to all three of you.
-- Lana has a distinct advantage over you.
-- Adam has a big advantage over Lana.
-- Adam has an even bigger advantage over you.
-- You are at a big disadvantage.  (Notice that one of your
numbers ... 1 ... can never come up unless one of the dice
falls off of the table.)


Here's how to figure it:

Ways to roll a 2:
1 ... 1

Ways to roll a 3:
1 ... 2
2 ... 1

Ways to roll a 4:
1 ... 3
2 ... 2
3 ... 1

Ways to roll a 5:
1 ... 4
2 ... 3
3 ... 2
4 ... 1

Ways to roll a 6:
1 ... 5
2 ... 4
3 ... 3
4 ... 2
5 ... 1

Ways to roll a 7:
1 ... 6
2 ... 5
3 ... 4
4 ... 3
5 ... 2
6 ... 1

Ways to roll an 8:
2 ... 6
3 ... 5
4 ... 4
5 ... 3
6 ... 2

Ways to roll a 9:
3 ... 6
4 ... 5
5 ... 4
6 ... 3

Ways to roll a 10:
4 ... 6
5 ... 5
6 ... 4

Ways to roll 11:
5 ... 6
6 ... 5

Ways to roll 12:
6 ... 6

Ralph is earning 2.8% commission