In　this　paper,　we　probe　the　pth　moment　exponential　stability　(p−ES)　of　stochastic　delayed　systems　subject　to　event-triggered　delayed　impulsive　control　(ETDIC),　where　the　impulsive　intensities　are　assumed　to　be　positive　random　variables.　Based　on　event-triggered　mechanism　(ETM)　in　the　sense　of　expectation,　some　new　sufficient　conditions　are　developed　to　ensure　the　stability　of　the　addressed　system　with　Zeno-free　behavior.　The　Lyapunov–Razumikhin　method　is　adopted　to　handle　the　time-varying　delay　in　continuous　dynamics,　and　the　concept　of　average　random　impulsive　estimation　(ARIE)　is　introduced　to　reduce　the　design　requirements　of　the　controller.　Especially,　the　proposed　ETDIC　strategy　not　only　generates　the　impulse　time　sequence　according　to　the　predesigned　ETM,　but　also　removes　the　limitations　on　the　size　of　time　delays.　Furthermore,　the　ETM　serves　as　a　solution　for　synchronization　problems　in　complex　neural　networks.　Finally,　two　examples　are　given　to　illustrate　the　effectiveness　of　our　conclusions.　©　2024　Elsevier　B.V.