Mutually Exclusive Events -Clarification

[PDEM200]

Hello,
Just wanted to make sure I understand the concept and follow-through on the example in Ch.2 pg.30

Point#1
Given 3 events(A,B,C), the probability that any one event occurs = P(A) + P(B) + P(C) - P(AB) -P(BC) -P(AC)-is this correct?

Piont#2
Also, can you advise on the impact of whether the events are independent or not (how does it impact the calc?). I understand that if mutually exclusive the formula would simplify to P(A) + P(B) + P(C) (I believe).
Thank you

 

[David Harper CFA FRM]

Paul,

http://learn.bionicturtle.com/images/forum/3_venn_circles.png

1. Note the venn has 7 "pieces" so you need to add back the P(ABC) to yours: P(A) + P(B) + P(C) - P(AB) -P(BC) -P(AC) + P(ABC)

2. I am not immediately sure if/how independence would impact. Independent btwn A&B, e.g., IIF P(A)*P(B) = P(AB). Therefore, *seems* to me independence neither implied nor required but i can only immediately see how to test for it.

David

append: although, i forgot the straightforward (uggh!): if independent, P(ABC) = P(A)P(B)P(C). We could just use that i suppose

 

[PDEM200]

Thanks for the clarification