# Probability intersections

So the the example in the book says that A is the event that a person lives at least ninty years and B is the event that a person lives at least 80 years.

Then it says that P(AB) = P (A) and that the overlap is "at least 90" which is A. But how could 90 which is larger be an intersection of 80?

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quasar987
Homework Helper
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hmm, perhaps you're confused with the definition of an intersection?

AB means A and B are realized. But if A is realized, then B is automatically realized for the simple reason that if a person lives 90 years or more, then it also lives 80 years or more. So every element of A is in B. This means that A a subset of B. So AB=A.

quasar987 said:
hmm, perhaps you're confused with the definition of an intersection?

AB means A and B are realized. But if A is realized, then B is automatically realized for the simple reason that if a person lives 90 years or more, then it also lives 80 years or more. So every element of A is in B. This means that A a subset of B. So AB=A.
Well, ok, but say I were to draw a venn diagram of living to at least 80 and then ond of living to at least 90. Then the one of at least 90 would have to be bigger than at least 80 so there's no way the interesection could be bigger then 80.

quasar987