FWIW this is what I think...

P(A) is the probability that 1 of the 2 bros in Division A will come in last. So P(A) = 2/6

P(B) is the probability that the brother in Division B will come in last. So P(A) = 1/6

Since P(A) and P(B) are mutually non-exclusive (non-mutually exclusive? all inclusive? what's the right term here?)...

P(A or B) = P(A) + P(B) - P(A and B) = 2/6 + 1/6 - (2/6)(1/6) = 44.4_%

Is that accurate? Did I blow it? It's been a looooooong time since undergrad.