How do you describe combined events without getting lost?
You’ve probably seen probability questions where one event is easy, then the question suddenly says and, or, or given that. That is where combined probability starts. You are no longer tracking one result by itself , you are tracking how groups of outcomes connect.
An event is a collection of outcomes you care about from a random situation. The sample space, written as U or sometimes S, is the full set of possible outcomes.
Probability uses set notation because events behave like groups inside a bigger group. If you are talking about event A and event B, then A ∪ B means outcomes that land in A, in B, or in both. A ∩ B means only the outcomes shared by both sets. A' means everything in the sample space that is outside A.
If two events cannot happen together, they are called mutually exclusive. In set language, that means A ∩ B = ∅, so their shared probability is P(A ∩ B) = 0.
The sneaky bit is the word or. In probability, or usually includes the overlap. So A ∪ B does not mean “exactly one of them”. It means at least one happens.
Think of A ∪ B like a playlist made from two artists. If a song appears on both artists’ collab lists, it still belongs in the combined playlist. Union keeps everything from either side.
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