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[ap-stat] Re: Independent/Mutually Exclusive Events
Posted:
Nov 18, 2005 11:28 PM
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> If 2 events are NOT independent then are they automatically mutually
> exclusive (and vice versa)?
>
Many events are neither independent nor mutually exclusive.
Take hair length and gender, for example. If you are betting on the gender
of the next person to walk around a corner, you would have about a 50%
chance of being correct with a guess of male.
If a friend who is standing around the corner is trying to help you out,
he or she might shout, "This next one has long hair!" Now, while there are
certainly a number of long-haired people of both genders, I think it's
safe to say long hair is more prevalent among females. At least in
Wisconsin. Outside of Madison. Taking this new information into account,
you might bet 'female.' You are not guaranteed to be correct, but you have
a better chance than if you bet male.
So the events "The person is male" and "The person has long hair" are not
independent. Knowing the person has long hair changes the probability of
their being male. Symbolically, P(male | long hair) not= P(male). But they
are not mutually exclusive, either. Both events can happen..
Corey
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