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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.  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.
 
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)/62=6/36=1/6