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In a dice, we have 6 sides, and a side can have 1 - 6 dots. The problem says that we have two dice, let's name them dice 1 and dice 2, and we need to find the probability of obtaining any sum (# of dots on dice 1 + # of dots on dice 2) when you randomly roll them. To do this, first find the total number of combinations.

Total # of comb. = [tex]6 \; \text{sides} \times 6 \; \text{sides}[/tex] = 36 combinations.

For letter (A.), it is asking for the probability of obtaining a sum of 4.

Dice 1: 1 and Dice 2: 3 so we get 1+3=4
Dice 1: 3 and Dice 2: 1 so we get 3+1=4
Dice 1: 2 and Dice 2: 2 so we get 2+2=4

So we have a total of 3 combinations that sum to 4.

The probability for letter (A.) is combinations that sum to 4 divided by Total # of comb. We get 3 divided by 36 or 3/36.

We do the same for letters (B.), (C.), (D.), and (E.) by counting the number of combinations that sum to the asked number.

Letter (B.): We can have the following combinations that sum to 6:

Dice 1: 1 and Dice 2: 5 so we get 1+5=6
Dice 1: 5 and Dice 2: 1 so we get 5+1=6
Dice 1: 2 and Dice 2: 4 so we get 2+4=6
Dice 1: 4 and Dice 2: 2 so we get 4+2=6
Dice 1: 3 and Dice 2: 3 so we get 3+3=6

The probability for letter (B.) We get 5 divided by 36 or 5/36.

Letter (C.): We can have the following combinations that sum to 7:

Dice 1: 1 and Dice 2: 6 so we get 1+6=7
Dice 1: 6 and Dice 2: 1 so we get 6+1=7
Dice 1: 2 and Dice 2: 5 so we get 2+5=7
Dice 1: 5 and Dice 2: 2 so we get 5+2=7
Dice 1: 3 and Dice 2: 4 so we get 3+4=7
Dice 1: 4 and Dice 2: 3 so we get 4+3=7

The probability for letter (C.) We get 6 divided by 36 or 6/36.

Letter (D.): We can have the following combinations that sum to 9:

Dice 1: 3 and Dice 2:6 so we get 3+6=9
Dice 1: 6 and Dice 2: 3 so we get 6+3=9
Dice 1: 4 and Dice 2: 5 so we get 4+5=9
Dice 1: 5 and Dice 2: 4 so we get 5+4=9

The probability for letter (D.) We get 4 divided by 36 or 4/36.

Letter (E.): We can have the following combinations that sum to 11:

Dice 1: 5 and Dice 2: 6 so we get 5+6=11
Dice 1: 6 and Dice 2: 5 so we get 6+5=11

The probability for letter (C.) We get 2 divided by 36 or 2/36.