Are Male/Female & ICU/Surgical Mutually Exclusive?

[soulstriss]

a hospital classifies some of the patents' files by gender and by type of care received (ICU and Surgical Unit).

the number of patients in each classification:

Gender // ICU // Surgical Unit
Male // 25 // 39
Female // 21 // 15

are the events "being female" and "being in the ICU" mutually exclusive?

are the events "being in the ICU" and "being in the surgical unit" mutually exculsive?


lost! please help.

 

[Focus]

This looks a bit like a homework question. Whats the problem here? The definition of mutually exclusive is that two events cannot happen at the same time, i.e. $$Pr(A \cap B)=0$$ for A and B mutually exclusive.

 

[statdad]

The definition of mutually exclusive is not that $$\Pr(A \cap B) = 0$$. Two events are mutually exclusive if their intersection is empty - that is, if they do not have any outcomes in common.
If we were talking about types of animals, the event '' is a mammal'' and the event ''is a reptile'' are mutually exclusive events

For the OPs question, ask this: is it possible for a person to be both female and in the ICU? Answering that will show whether they are mutually exclusive.

 

[Focus]

The definition of mutually exclusive is not that $$\Pr(A \cap B) = 0$$. Two events are mutually exclusive if their intersection is empty - that is, if they do not have any outcomes in common.
If we were talking about types of animals, the event '' is a mammal'' and the event ''is a reptile'' are mutually exclusive events

For the OPs question, ask this: is it possible for a person to be both female and in the ICU? Answering that will show whether they are mutually exclusive.

Sorry I did not say that the definition was $$\Pr(A \cap B) = 0$$, I ment that for A and B mutually exclusive $$\Pr(A \cap B) = 0$$, which is true! Thus you can eliminate any intersection of events that have possitive (non-zero) probability.

 

[statdad]

You wrote (I have inserted the bold formatting)
"The definition of mutually exclusive is that two events cannot happen at the same time i.e. $$P(A \cap B) = 0$$ for A and B mutually exclusive.''

As written, the 'cannot happen at the same time' in your post gives the impression that the definition you wrote is based on probability, not on an empty intersection. The zero probability is a consequence of the events' mutual exclusivity, not the definition.

 

[Focus]

No I don't think it does, when two events cannot happen at the same time, it does not matter which probability measure you take!

http://www.britannica.com/EBchecked/topic/399902/mutually-exclusive-event
http://en.wikipedia.org/wiki/Mutually_exclusive
Both agree with me here.

 

[statdad]

I think you are missing my point. I am well aware that what you say is true regardless of whether the underlying distribution is discrete, continuous, or mixed. My point is that the definition of mutually exclusive can be made referring to the events [(measurable) sets] themselves - probability is not needed for this at all.
And, lest we forget the purpose of these postings, the OP should have more than enough information to be able to answer the original question.