There are two security guards for a large establishment. Each carries a pager activated by detectors in the buildings. Let X be the event that Guard 1 reports the alert. Let Y be the event that Guard 2 reports the alert. No, both can report.
Tree diagrams are helpful in organising calculations that involve several stages.
Each segment in the tree is one stage of the problem and the probabilities on the branches from each point must sum to 1. The probability of reaching the end of any complete path is the product of the probabilities written on its branches. There are 8 outcomes. An event is any subset of outcomes. Both C and D can happen at once.