So you're going to have 36 combinations, because for each number 1-6 which may be rolled for the first roll, you're going to also have 6 other possible numbers for the second roll. This gives you 6 * 6 or 36. So you could define the entire sample space, but you could also just list the sample space with all the sums less than 7 that way you don't have to list all of the sample space, since you already know how many combinations there are going to be

Let's start with the case that you roll a 1, for the first roll:

1+1 = 2

1+2 = 3

1+3=4

1+4=5

1+5=6

These are the only combinations that will be less than 7 so stop here

Now do the case where you roll a 2, for the first roll

2+1 = 3

2+2= 4

2+3 = 5

2+4 = 6

The next roll will result in a roll greater than 6. This time there were only 4 combinations which is one less than the previous. This makes sense, since you're still increasing in intervals of 1, except the starting number is increasing by 1, meaning as the first roll increases, the amount of combinations with that starting roll that are below 7, will decrease by 1. So this means that:

1: 5 combinations

2: 4 combinations

3: 3 combinations

4: 2 combinations

5: 1 combination

6: 0 combination

This means there are going to be a total of 15 combinations which are less than 7, that means there are 36-15 combinations which are greater than or equal to 7. This simplifies to 21/36 which simplifies to 7/12. This can also be expressed as: 0.5833

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2 years ago