  The scenario of light gluinos and light sbottoms was advocated to explain the
discrepancy between the measured and theoretical production of $b$ quarks at
the Tevatron. This scenario will have model-independent predictions for $Z\to
q\bar q \tilde{g} \tilde{g}$ at the $Z^0$-pole, and $e^+ e^- \to q\bar q
\tilde{g} \tilde{g}$ at LEPII. We show that the data for $Z\to q \bar q g^* \to
q\bar q b \bar b$ at LEPI cannot constrain the scenario, because the ratio
$\Gamma(Z \to q\bar q \tilde{g} \tilde{g})/ \Gamma(Z \to q \bar q g^* \to q\bar
q b \bar b) = 0.15 - 0.04$ for $m_{\tilde{g}}= 12-16$ GeV is smaller than the
uncertainty of the data. However, at LEPII the ratio $\sigma(e^+ e^- \to q\bar
q \tilde{g} \tilde{g})/ \sigma(e^+ e^- \to q \bar q g^* \to q\bar q b \bar b)
\simeq 0.4 - 0.2$ for $m_{\tilde{g}}= 12-16$ GeV, which may give an observable
excess in $q\bar q b\bar b$ events; especially, the $4b$ events.
