Re: p(A1 U A2 U ...UAk) = p(1) + p(2) + ... + p(k)


BW wrote:
Despite my best efforts, I know that some students still walk
away believing that independence and mutual exclusivity are the same thing.

RF wrote:

How true! A diametrically OPPOSITE view.

That's why/how I came upon the statement

As I always tell my students that the concepts of "mutually
exclusiveness" and "independence" of events are themselves
mutually exclusive -- because you can NEVER have both.

That forces them to think twice about the non-overlapping
characteristic of mutual exclusiveness.

I forgot to add this: I think that the reason many students believe that mutual exclusivity and independence are the same thing is that they don't *think* about what the words mean. They just treat them as meaningless labels--they might just as well be called "gezortenblatt" and "jabberwocky". ;-) And, if the words carry no meaning, students have to rely on rote memory.

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

Relevant Pages

  • Re: p(A1 U A2 U ...UAk) = p(1) + p(2) + ... + p(k)
    ... away believing that independence and mutual exclusivity are the same thing. ... Outer Mongolia where Luie lives -- they you might think you are ... Outer Mongolia doesn't quite depend on whatever YOU do in the USA. ...
    (sci.stat.math)
  • Re: Independent versus Mutually Exclusive Events
    ... No one has yet mentioned in this thread that mutual exclusivity has nothing to do with the probability measure. ... As others have pointed out, by definition, two events are independent if and only if the probability of the joint event is the product of the probabilities of the individual events. ... The interpretation of independence is that one event "tells you nothing" about the other. ...
    (sci.math)