If event A is a subset of event B, is it safe to say P(B-A) = P(B) - P(A)? In general, is it safe to say P(A+B) = P(A) + P(B), P(A*B) = P(A)*P(B), P(A/B) = P(A) / P(B), etc.?
Ok point taken. Anyways, here's a problem I'm kinda stumped on:
"Let , ,..., be a sequence of increasing events of a sample space, i.e. is a subset of , .
Let , , . Note that .
a. Use the events , ,... to prove that . This proves that probability is a continuous function, because the increasing sequence of events { , } is a convergence sequence."
Does anyone have any idea how to prove lim P( ) = P[lim ( )] in general? I'll be happy if you can show me that; no need to help me completely for that whole part.