Question

What is the theoretical probability of rolling a sum of 10 on one roll of two standard number cubes?

Answer 1

The sample space has 36 possible combinations of numbers. These can be set out in column form as follows:
6,6 5,6 4,6 3,6 2,6 1,6
6,5 5,5 4,5 3,5 2,5 1,5
6,4 5,4 4,4 3,4 2,4 1,4
6,3 5,3 4,3 3,3 2,3 1,3
6,2 5,2 4,2 3,2 2,2 1,2
6,1 5,1 4,1 3,1 2,1 1,1
Find the number of combinations summing to 10, then divide that number by 36.

Answer 2

How many ways are there for x + y = 10 such that 1 < x <= 4 and 4 < y <= 6?

4-6, 5-5, 6-4. So the smallest number that can be used to add the rolled numbers to 10 is a 4 and the largest possible number is a 6. Any number less than 4 cannot be added to any number in the interval [1, 6] such that the sum is 10. Hence there is only 3 possible ways for the sum to be 10.

Now we must find all possible sums. A 1 on one die can be rolled and there is 6 different numbers that the other die can die may roll. This gives us 6 combinations with the number 1 in it; 1-1, 1-2, 1-3, 1-4, 1-5, 1-6. Now if one die rolled 2, then there is also 6 ways for 2 to be combined with the 6 different numbers the second die rolls; 2-1, 2-2, 2-3, 2-4, 2-5, 2-6. This will be the case for every number hence giving us 6 x 6 = 36 total combinations.

Therefore the probability of rolling a sum of 10 on two standard dice is:\[\bf P=\frac { possible\ ways \ of \ adding \ 10 }{ All \ possible \ sums }=\frac{ 3 }{ 36 }=\frac{ 1 }{ 12 }\]

@xkylex

Answer 3

Woah!

Answer 4

Thanks all of you!

Answer 5

You all deserve medals.

Answer 6

You're welcome :)