  The $S=1/2$ Heisenberg chains with bond alternation and randomness on the
strong bonds are studied by the density matrix renormalization group method. It
is assumed that the odd-th bond is antiferromagnetic with strength $J$ and
even-th bond can take the values $\JA$ and $\JF$ $ (\JA > J > 0 > \JF)$
randomly. The ground state of this model interpolates between the Haldane and
dimer phases via a randomness dominated intermediate phase. Based on the
scaling of the low energy spectrum and mean field treatment of the interchain
coupling, it is found that the magnetic long range order is induced by
randomness in the intermediate regime. In the magnetization curves, there
appears a plateau at the fractional value of the saturated magnetization. The
fine structures of the magnetization curves and low energy spectrum are
understood based on the cluster picture. The relation with the recent
experiment for (CH$_3)_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x})_3$ is discussed.
