P(Sum of the two dice is not 9 and not 6)

Question

I need help in getting the solution to the statistics question

Answer 1

Use the following table to model problems for rolling the pair of dice:

1st dice (technically it's called die)

1 2 3 4 5 6

---------------------------------

1 | 2 3 4 5 6 7

2 | 3 4 5 6 7 8

3 | 4 5 6 7 8 9

4 | 5 6 7 8 9 10

5 | 6 7 8 9 10 11

6 | 7 8 9 10 11 12

The column is the 2nd die

So of the 36 possible outcomes, there are

5 in the first row,

5 in the 2nd row,

4 in the 3rd row,

4 in the 4th row,

4 in the 5th row,

5 in the 6th row

TOTAL is 27

27/36 = 3/4 = 75%

-----------------------------

the other way to figure it without the table is

like this...

ways to get 6: (1,5) , (2,4) (3,3) (4,2) (5,1)

ways to get 9: (3,6),(4,5)(5,4)(6,3)

there are 9 ways that must be AVOIDED, so 36-9=27

outcomes of interest...

27/36 = 3/4 = 75%