Modelling a union of two Bernoulli events

Modeling
5

This is also wrong, but in the more subtle way. I am counting the same data twice. The correct answer is this:

data {
  int<lower=0> n_nn;
  int<lower=0> n_pn;
  int<lower=0> n_pp;
  int<lower=0> n_np;
}

transformed data {
  int nd[4];
  nd[1] = n_nn;
  nd[2] = n_pn;
  nd[3] = n_np;
  nd[4] = n_pp;
}

parameters {
  real<lower=0, upper=1> pA;
  real<lower=0, upper=1> pB;
}

transformed parameters {
  simplex[4] s;
  s[1] = (1-pA) * (1-pB);
  s[2] = pA * (1-pB);
  s[3] = pB * (1-pA);
  s[4] = pA * pB;
}

model {
  nd ~ multinomial(s);
}

@DouglasBoubert your answer is 100% correct, simple and beautiful. For my further work I need a form where I can put further constraints, since the model I work on has a third event, “T”, which manifests itself only with counts on n_pp. This is where this seems more useful.