# I'm sure YOU are right...

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Posted by Joel on September 24, 2002 at 18:05:52:

In Reply to: are you sure??? or am I wrong again??? posted by T.Gracken on September 23, 2002 at 19:18:37:

: : : Suppose that the population of a certain city is 40% male and 60% female. Suppose also that 50% of the males and 30% of the females smoke. Find the probablility that a smoker is a male.

: : Hello, Brett!
: : Boy, this is really hard...

: : Suppose there 100 people (try it when percents are involved).
: : Then there are 40 males and 60 females.

: : 50% of the males smoke -- um, that's HALF of them... uh... 20 ?

: : And "20 out of 100" is...? (Where's my calculator?)

: : ~~~~~~~~~~

: As usual, when it comes to probability, I am probably looking at the problem incorrectly...

: but, using your example (100 people considered), then if there are 20 male smokers, you can reason that there are also 18 female smokers.

: so out of 100, 38 people smoke. also, if we consider the question "what is the probability that a smoker is male?", I read this as "out of 38 people, what is the probability that one of them is a male", or in other symbols, 20 out of 38 are male (from this group),

: ...so I see the probability of a smoker being male as 10/19 (or appx. 0.53).

: I just see this as a probability of an event given "an event". [i.e. P(E|A)=P(smoker is male|smoker)]

: just my interpretation... (as stated above, probability is not my field)

Soroban answered the question, "What is the probability that a person selected at random from the entire population of all people, males and females, smokers and nonsmokers is BOTH male and a smoker?" But that was not Brett's question.

The population for Bretts question, "What is the probability that a smoker is male" should be limited to smokers only. T Gracken correctly answered the question "What is the probability that an individual selected from the population consisting of all smokers is a male?"

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