P(AB) = (1/3)(5/9) = 5/27.
P(AB) is the probability that the same vendor gets both orders and that v2 gets at least one. There is only one point for which this is true (v2,v2)
OKP(AUB) = 1/3 + 5/9 - 1/9 = 7/9.
why do you have 1/9 for P(AB) here when you have something wrong when asked for it directly?