This is actually a questionable conclusion due to an assumption: You're assuming that the probability of the 10 combinations you listed are equal to one another (that each one has a 1/10 chance of being the contents of the chest). However, if the two specific patterns in each chest are rolled independently of one another (and not as some form of set pair system), then they do NOT have equal probabilities of being what you get.
If each chest has 2 patterns of four possible classes, selected independently at random, then there are 4x4=16 possible results, each with a 1/16th chance of occuring. Upon opening the chest, a (1)Trooper + (2)JK combination will appear the same to us as a (1)JK + (2)Trooper combination. However, they are technically 2 different results out of the pool of 16. This means that the odds of getting a specific mixed combo of patterns (such as JK/Trooper) is actually 1/16+1/16 = 1/8, because there are two permutations of that combo...two results out of 16 that will give the same combo. A specific same-type combo (Smuggler/Smuggler) still only has a 1/16th chance, as only one result of two independent rolls will generate it.
If that is the case, then each chest only has a 1/16 chance of double Smuggler and a 6/16 chance of Smuggler + Different class (S+JK, S+JC, S+T, JK+S, JC+S, T+S). Apply it to the original issue of the odds of 7/8 Smuggler drops and you get :
(S+S) * (S+S) * (S+S) * (S+Other) -> 1/16*1/16*1/16*6/16 = 6/65536
Multiply by the 4 possible permutations of chest order (The S+Other chest could be the first, second, third or fourth one) -> 6/65536 * 4 = 24/65536 = .000366, or .0366%.
At the end of the day, only Bioware actually knows how their loot tables are seeded, and if the rolls for patterns are random and independent or not. I personally think there is something slightly off, but I reserve judgment until I have enough hard data myself to make a real analysis.