Formula when at least two events are true out of three ↩

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Consider three events in a sample space , and . The formula for when at least two of the events are true is this:

Formulation

There are two cases that satisfy the criterium:

When all three are true

Combine them with intersection:

When one of them is false

One needs to be false and the others are true, this means 3 cases using a complement and intersection:

And we combine these using union:

Full combination