Using the data accumulated in 2002-2004 with the DO detector in proton-antiproton collisions at the Fermilab Tevatron collider with centre-of-mass energy 1.96 TeV, the branching fractions of the decays B -> bar{D}_1^0(2420) mu^+ u_mu X and B -> bar{D}_2^{*0}(2460) mu^+ u_mu X and their ratio have been measured: BR(bar{b}->B) cdot BR(B-> bar{D}_1^0 mu^+ u_mu X) cdot BR(bar{D}_1^0 -> D*- pi+) = (0.087+-0.007(stat)+-0.014(syst))%; BR(bar{b}->B)cdot BR(B->D_2^{*0} mu^+ u_mu X) cdot BR(bar{D}_2^{*0} -> D*- pi^+) = (0.035+-0.007(stat)+-0.008(syst))%; and (BR(B -> bar{D}_2^{*0} mu^+ u_mu X)BR(D2*0->D*- pi+)) / (BR(B -> bar{D}_1^{0} mu^+ u_mu X)cdot BR(bar{D}_1^{0}->D*- pi^+)) = 0.39+-0.09(stat)+-0.12(syst), where the charge conjugated states are always implied.
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