The discussion revolves around proving inequalities related to simple probability, specifically the relationships between the probabilities of events A and B, including their intersection and union.
Participants are exploring various interpretations of the inequalities and discussing the implications of set relationships on probability. Some guidance has been offered regarding the subset relationships and how they relate to the probabilities, but no consensus has been reached on the proofs themselves.
There is an emphasis on understanding the definitions of sets and probabilities, as well as the constraints of working within the interval [0,1] for probabilities. Participants are also navigating the definitions of union and intersection in the context of the problem.
So what you're saying is that I have to show that A is a subset of AUB. This is done by definition that AUB=A+B therefore A is a subset of AUB and it follows (as you said) that P(A) is less than or equal to P(AUB). Correct? What would I do to prove the intersection is less than A?lanedance said:be careful, probabilities are scalar numbers in the interval [0,1], whilst A & B are sets
so if you can show
A \subseteq B
it follows directly that
P(A) \leq P(B)
as every event in A is also in B