Solution
= Solution
Letting $t\to\infty$ in the <cumulative incidence function> gives \b[the probability that the observed first event is of type A]:
$$
\boxed{\Pr(J=A)=\Pr(T_A<T_B)=\frac\alpha{\alpha+\beta}.}
$$
This is the sense of occurrence in the <competing risks model>. If one instead followed the latent exponential $T_A$ even after B, its eventual-occurrence probability would be one; that is a different question from observing A before the competing event.