The quantum jump statistics for the three stable isotopes ofMg+ have been studied experimentally. Single ions ofmagnesium were held and laser cooled in a Penning trap. Quantumjumps were observed by collecting the resonance fluorescencenear 280 nm from the cooled ion.The jump rate was analysed to find ratios of the average time theion spends fluorescing, `on' time, to the average time itspends in the dark state, `off' time: for both 24Mg+and 26Mg+ this value was found to be 15.9±1.2, in agreement with a theoretical value of 16.0. Thepresence of hyperfine structure in 25Mg+ means thatwhile the jump rate for 24Mg+ and 26Mg+remains unaltered for both available cooling transitions, forthe odd isotope the on to off ratio is predicted to be 11.8and 22.8 for the lower and upper transitions respectively.Experimental values for these ratios were found to be 10.2 ± 0.7 and 22.0 ± 0.6.The occurrence of so-called nuclear jumps in 25Mg+is investigated qualitatively. These rare jumps are produced asa result of the hyperfine splitting, which is only present inthe odd isotope. Although the data indicate some evidence forthis type of jump, it is not possible to draw any firmconclusions due to the small number of events observed.