Hey Chris,
Great question, and I think it hinges on how you interpret the term "outcomes". You're right that there are only 4 potential sums, but I'd look at "outcomes" as to define the number of sequences. The reason for that is that each sequence has the same probability, so that allows you to calculate. Since there are only 8 potential sequences we can even just list them out:
0, 0, 0 ---> sum to 0
0, 0, 1 ---> sum to 1
0, 1, 0 ---> sum to 1
1, 0, 0 ---> sum to 1
0, 1, 1 ---> sum to 2
1, 0, 1 ---> sum to 2
1, 1, 0 ---> sum to 2
1, 1, 1 ---> sum to 3
So there are 8 sequences, but only 4 sums. I'd look at "outcomes" as meaning the entire sequence and not just the sum result, because then you can calculate mathematically:
8 total sequences is your denominator
Then, calculate how many ways to get 2 as your numerator, either listing out the sequences that work, or using permutations:
How many ways to arrange two 1s and a 0?
N = 3; one repeat:
3!/2! = 3
So there are 3 sequences that add to 2 out of 8 sequences total for a probability of 3/8.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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