Simple probability question about SNPs

I have a (simple?) question concerning SNP probabilities: if I know I have an heterozygous SNP, let's say rs123456(A;C), then what's the probability that my brother will be heterozygous on the same SNP?
 

EDIT: added possibly correct solution (below the original wrong solution)
 

So probability is calculated as:
son's heterozygous outcomes / total son's outcomes
 

Let's compute the total part first.
Single parent: combinations with repetitions of 2 elements (A,C) in 2 places (my parents chromosomes). That's C(n+k-1,k) = C(3,2) = 3
(Easier if we just list them AA, AC, CC).
 

Given 2 parents, we need to make the cartesian product to obtain all total pairs: 3x3 = 9
 

However we know that each pair must be able to give het. son, so we have to remove AA-AA and CC-CC pair's. So total number is 9 - 2 = 7.
(AA-AC, AC-AA, AA-CC, CC-AA, AC-AC, AC-CC, CC-AC)
 

Total son's outcomes: for each parents outcome, 4 outcomes for the son are possible (cartesian product). So in total that's 7 * 4 = 28.
 

Let's compute the possible het. son's outcomes.
For this, we just count the number of het. outcomes in the above list.
(AA-AC [2], AC-AA [2], AA-CC [4], CC-AA [4], AC-AC [2], AC-CC [2], CC-AC [2])  

That's' 18.
 

So final value is 18/28, about 64%.

However this assumes any SNP variant may appear with same probability in parents. To compute the probability correctly, do I just need to just weight each SNP variant in parent according to the data available on SNPedia?
 

(Original WRONG solution)

My hypothesis is that since I am heterozygous, my parents possible SNP values would be :
 

The total number of possible combinations for a son are (2^2) * 4 = 16
While the number of heterozygous combinations are 4 + 4 + 2 + 2 = 12
 

So the probability seems to be 75%