Classification targets with heterogenous meanings
Will it be P(5+ and reawaken), or will it be something else?


The events are not independent, so one cannot assume that p(A and B) = p(A) * p(B). 

Let's denote the events as follows:


A = reawakens (not A = remains dormant)
B = purchases at least 5 times


The event "reawakens and purchases more than 5 times" is "A and B". In general we have:

p(A and B) = p(A/B) p(B)
p(A and B) = p(A/B) (p(A and B) + p(not A and B))


But it's impossible for a customer to stay dormant and buy anything, so:

p(not A and B) = 0 


Which gives us:

    p(A and B) = p(A/B) p(A and B)
    p(A/B) = 1


Then we obtain:

p(A and B) = p(B)


Note that this makes sense intuitively: the probability of buying at least 5 times is the same as awakening and buying at least 5 times.

Currently the labels of the two models overlap so I don't think you can infer much from combining their outputs. A way to make it usable would be to make the first model consider only awakening customers in order to avoid the overlap. But it might be more useful to train a single joint model to get a clear picture of your data. In general such a model would classify between 4 categories:


not A and not B
not A and B
A and not B
A and B


But since p(not A and B) = 0 there are actually only 3 labels corresponding to:


stays dormant
awakens and buys less than 5 times
awakens and buys at least 5 times