= Solution
Take the event to mean three smoking-free weeks in succession, $Y_{i1}=Y_{i2}=Y_{i3}=1$. The initial cumulative count is zero. Along this path it equals $0,1,2$ in weeks one, two, three, respectively. In the <cumulative-response logistic model>, define
$$
\pi_c=\frac{\exp(-1.417630+0.001224(20)+0.399296c)}
{1+\exp(-1.417630+0.001224(20)+0.399296c)}.
$$
The <chain rule for probabilities> then gives
$$
\boxed{\Pr(Y_{i1}=Y_{i2}=Y_{i3}=1\mid S_i=0,A_i=20,T_i=0,\mathcal H_{i0})
=\pi_0\pi_1\pi_2\simeq0.01911.}
$$
The three conditional <probabilities> are approximately $0.19891,0.27015,0.35559$. If “stop during the first three weeks” instead means at least one smoking-free week by week three, its different event has <probability> $1-(1-\pi_0)^3\simeq0.48590$: along the all-failure path the cumulative count stays zero. Stating the event resolves this wording ambiguity.
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