  An updated fit to the precision electroweak data and to the direct
measurement of the top quark mass $m_t$ provides significant constraints on
$m_t$ and on the Higgs boson mass $M_H$: $m_t/\text{GeV}=172\pm 6$ and
$\log_{10}(M_H/\text{GeV})=2.16\pm 0.33$, with an error correlation $\rho=0.5$.
We integrate the $(M_H, m_t)$ probability distribution found in this analysis
over various zones of the $(M_H, m_t)$ plane defined by one-sided experimental
and theoretical bounds on the Higgs boson mass, both in the Standard Model and
in its minimal supersymmetric extension. The comparison of the cumulative
probabilities gives interesting information on the likelihood that the true
value of $M_H$ is compatible with different theoretical scenarios.
