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Math Help - a conditional probability problem discussion

  1. #1
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    a conditional probability problem discussion

    this is a problem about condition probability . I am not asking for solutions (I have the solution already but dont understandt) but I hope to have some discussion about this problem

    In a city, with equal number of male and female. 10% of male regarded as 'good-looking' while 10% of female regarded as 'good-looking'. They form couples randomly.

    Given that a member of a couple is 'good-looking', find the probability that the other member is also'good-looking'


    I was not able to do anything when I first saw this question. and I am now not able to understand when I see the solution.
    I hope someone will teach me how to classify a problem, I want to have a clearer concept on probabilty. I don't want every time every old similiar questions make me feel like the new one ... it's painful

    For example this one, the solution sets two events

    M: good looking male
    F: good looking female

    then they go straight to a formula, - The required probability = P( L & G | L U G)

    why?? why?? why isn't it P(G | L) + P(L | G)? I simply don't understand why I am wrong and how he determines the formula.

    or why it can't be P(L & G | L) + P(L & G | G). Why??

    I am in a big headache.

    I understand the concept after reading the theories for many many times, but I now I don't really think I understand that
    Last edited by kennysiu; March 23rd 2012 at 05:02 PM.
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  2. #2
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    Re: a conditional probability problem discussion

    Let G=good looking and N= not good looking. Then if we pick a couple at random we either get GG (p=0.1x0.1) GN (p=0.1x0.9) NG (p=0.9x0.1) or NN (p=0.9x0.9) We are told we get one of the first three (p=0.01+0.09+0.09=0.19) and we want the probability that it is the first of these (p=0.01). Hence answer is 0.01/0.19.
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  3. #3
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    Re: a conditional probability problem discussion

    Sometimes it helps to forget about the formulas and just think about what is going on. In this case, we have couples formed at random from the population. How one partner looks has no bearing on the way the other partner looks, i.e. these are independent events. What that means is that whether A is 'good-looking' or not, B will still have that same 1/5 chance of being 'good-looking'.
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  4. #4
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    Re: a conditional probability problem discussion

    Quote Originally Posted by cshanholtzer View Post
    What that means is that whether A is 'good-looking' or not, B will still have that same 1/5 chance of being 'good-looking'.
    Where does the number 1/5 come from?
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  5. #5
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    Re: a conditional probability problem discussion

    20% of the population is good looking, i.e. 1/5. Or if the couples are required to be mixed gender 10% of half the population whether male or female still yields 1/5.
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  6. #6
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    Re: a conditional probability problem discussion

    Quote Originally Posted by cshanholtzer View Post
    20% of the population is good looking, i.e. 1/5.
    The OP says
    Quote Originally Posted by kennysiu View Post
    10% of male regarded as 'good-looking' while 10% of female regarded as 'good-looking'.
    This means that 10% of the population is good looking.
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  7. #7
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    Re: a conditional probability problem discussion

    I was reading that as 10% of males and 10% of females, i.e. 20% of people.
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  8. #8
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    Re: a conditional probability problem discussion

    Let the total number of males in the city be m and the total number of females be f. Then there are 0.1m good-looking males and 0.1f good-looking females. The total number of good-looking people is 0.1m + 0.1f = 0.1(m + f), i.e., 1/10 of the total population m + f.
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  9. #9
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    Re: a conditional probability problem discussion

    Oh boy do I feel dumb now. Thanks for setting me straight.
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