In the paper new bounds are given for the probability of the union of events. For this purpose new concept of hypercherry trees was introduced. The concept of cherry trees has been introduced earlier by A. Prékopa and J. Bukszár and the concept of m-multitree has been introduced earlier by J. Bukszár. These hypergraph structures were applied successfully for defining bounds on the union of events, too. All these bounds can be regarded as generalizations of the upper bound introduced by D. Hunter by means of maximum weight spanning tree and so all these bounds were upper bounds. I. Tomescu introduced the concept of hypertrees in the framework of uniform hypergraphs and by means of these new hypergraph structures he was able to define not only upper but also lower bounds on the probability of union of events. The new bounds of the paper are the improvements of Tomescu's lower and upper bounds in the same sense as the upper bounds by A. Prékopa and J. Bukszár were improvements of Hunter's upper bound. The efficiency of the new bounds is illustrated on some test examples according to a special reliability system.
