Lately I've been doing statistics revision and I've realised that I'm not really
fully clear on all of the rules and how they work, hence I was hoping someone might be able to talk me through where I am going wrong.
I think it's maining when it comes to intersect (n) and union (u) which confuses me. I know that intersect is obviously where the 2 events intersect (therefore when something AND something else happen) and union is when one event OR the other occur. I've found no problem in placing these on a venn diagram concerning two events and finding the appropraite values from this.
However when I get questions like "Given that P(A) = 0.7, P(B) = 0.4 and P(AuB) = 0.8 find the following:
a) P(AnB) "
Now for this I would think that it'd be 0.7 x 0.4 as I always remember from lower probability that AND is x and OR is plus. However I find that according the my text book I should be doing:
P(AnB) = P(A) x P(B) - P(AuB)
I recognise this as the addition rule rearranged however I still do not understand exactly why I am using this and why I cannot use the multiplication rule - is it something to do with the fact that it's P(AnB) = P(A|B) x P(B) or something?
I'm still not clear on the workings of all this. Do we change things depending on if an event is independant or is mutually exclusive? If P(AnB) > 0 then is the event independant because it has a cross over between the two?
I just find myself a bit lost and confused at times because I want to follow the old "multiply along the branches" of tree diagrams method and feel I cannot differienciate between when to use one method over another.
Any explanation of where I'm going wrong would be of much help, thank you very much.