Which set has more people: those older than 80 or those older than 90?

[VonWeber]

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?

 

[quasar987]

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

This is how you should think about this:

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.

 

[VonWeber]

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

This is how you should think about this:

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]

The one of "at least 90" would be smaller than the "at least 80". In fact it is a subset of the "at least 80" one.

Consider B, all the people on Earth who are older than 80 and A, all those who are older than 90. Which set has more people do you think? It's B of course, since it has all those in A PLUS all the people whose age is btw 80 and 90.