= Solution
The positive intercept means the fitted baseline probability for untreated women exceeds $1/2$. The positive coefficient $\widehat\beta_S=0.1854$ makes each fitted male log odds exceed the corresponding female log odds, while $\widehat\beta_T=-0.3698$ makes treatment lower the fitted log odds for either sex. Numerically the fitted probabilities are approximately
$$
\widehat p_{F0}=0.701,
\quad\widehat p_{F1}=0.619,
\quad\widehat p_{M0}=0.739,
\quad\widehat p_{M1}=0.661.
$$
Their order is $F1<M1<F0<M0$, which differs from the observed order $F1<M0<M1<F0$. The additive model therefore cannot reproduce the observed ordering.
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