Joint probability
Though mutually exclusive cases are simple to work upon, most of the actual problems do fall under the category of non-mutually exclusive events. By using the joint appearance, we can predict the event outcome. For example, if emails messages present the word like lottery, which is very highly likely of being spam rather than ham. The following Venn diagram indicates the joint probability of spam with lottery. However, if you notice in detail, lottery circle is not contained completely within the spam circle. This implies that not all spam messages contain the word lottery and not every email with the word lottery is spam.
In the following diagram, we have expanded the spam and ham category in addition to the lottery word ...
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