The rates are measured per hadronic Z(0) decay for gluon splitting to b (b) over bar quark pairs, g(b (b) over bar), and of events containing two b (b) over bar quark pairs, g(4b), using a sample of four-jet events selected from data collected with the OPAL detector. Events with an enhanced signal of gluon splitting to b (b) over bar quarks are selected if two of the jets are close in phase-space and contain detached secondary vertices. For the event sample containing two b (b) over bar quark pairs, three of the four jets are required to have a significantly detached secondary vertex. Information from the event topology is combined in a likelihood fit to extract the values of g(b (b) over bar) and g(4b), namelyg(b (b) over bar) = (3.07 +/- 0.53(stat) +/- 0.97(syst)) x 10(-3),g(4b) = (0.36 +/- 0.17(stat) +/- 0.27(syst)) x 10(-3).
