I would like to know what the probability of rolling a 10 or larger would be with a pair of dice

## Consider rolling a pair of dice. What is the probability of rolling a 10 or larger?

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# 1 Answer

Hi Again Brittany;

How many possible combinations ≥ 10.

Let's begin with this...

If one of the die's is a 1, then the results cannot be ≥ 10.

If one of the die's is a 2, then the results cannot be ≥ 10.

If one of the die's is a 3, then the results cannot be ≥ 10.

If one of the die's is a 4, then if the other die is a 6, the result is =10.

If one of the die's is a 5, then if the other die is a 5 or 6, the result is ≥ 10.

If one of the die's is a 6, then if the other die is a 4, 5 or 6, the result is ≥ 10.

Here are the possible combinations...

1. 4,6

2 6,4

3. 5,5

4. 5,6

5. 6,5

6. 6,6

The quantity of combinations are 6

^{2 }. Six represents the quantity of sides, 2 represents the quantity of dice. If there are seven sides of three dice, the equation would be 7^{3 }.6/36 combinations are ≥ 10, 1/6.

There other way to analyze this is as follows...

If one of the die's is a 4, then if the other die is a 6, the result is =10.

ONLY ONE POSSIBLE COMBINATION.

If one of the die's is a 5, then if the other die is a 5 or 6, the result is ≥ 10.

ONLY TWO POSSIBLE COMBINATIONS.

If one of the die's is a 6, then if the other die is a 4, 5 or 6, the result is ≥ 10.

ONLY THREE POSSIBLE COMBINATIONS...

(1 + 2 + 3)/6

^{2}=6/36=1/6