Hello everybody here at GMATClub. As you all can see, this is my first post, although I have been browsing the forum for some time already. I would like to start by saying that I think this forum is a wonderful comunity and provides so much help to GMAT strugglers alike.
I have the following to say.
A
In the solution explanation for example question 7 of the probability lesson under GMATClub courses (I can't add a link due to spam prevention) it's stated that the events are not mutually exclusive (correct) but it's also explained that the events are independent. This however is odd as in the explanation of the Event Types and Sets Analogy theory under sub heading Compatible vs. Incompatible (Mutually exclusive) Events it is stated that "Note that mutually exclusive events are independent." This directly contradicts the statement in the solution explanation. I am not very strong on probability theory let alone mathematical concepts and am therefore doubting which statement to believe; I'd put my money on the statement of the theory. Could anyone clarify?
B
As I understand it, the probability theory necessary for GMAT exercises the following is important to know with regard to when to use the NOT Tool, AND Tool, and most specifically which type of OR Tool -- p(A OR B)=p(A)+P(B) vs. p(A OR B)=p(A)+P(B)-P(A AND B) --
There are 4 basic types of events (incompatible, compatible, independent and dependent) of which some are mutually exclusive and some are not mutually exclusive. I suspect an overlap between some of these event types exists and therefore I have the following questions with my suspicion indicated between brackets:
1 mutually exclusive event = independent event (yes, see first issue in this post)
2 not mutually exclusive event = compatible event (yes, derivative of 1)
3 can an event be both compatible and mutually exclusive? (no, derivative of 2)
4 can an event be both compatible and independent (no, derivative of 3)
5 mutually exclusive events consist of incompatible and independent events (yes)
6 compatible events consist of dependent events (yes)
There are a total of 4! (24) combinations to make I guess (combinatorics)

but I am not going to ask all of them, these 6 cover the basics I guess.
I realise that I may be juggling with all the terms and am therefore confusing myself even further, but the reason why I'm juggling is because I figured it would be helpful to map out the event types and their corresponding actions in a sort of flow chart to have a structured way of tackling all probability questions except combination, expectation and distribution probabilities as those have their own structured method.
I have made a similar flow chart for combinatorics questions and I think it works pretty well. If anyone is interested I can post this flow chart.
Thanks your help!