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Math Help - 3 Stats problems... need help

  1. #1
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    3 Stats problems... need help

    Hello,


    This is my first post here. I'm in need of some help understanding these three problems.

    #1. Determine all joint probabilities from the following.

    P(A)= .8
    P(BlA)= .4
    P(Ac)= .2
    P(BlAc)=.7

    read the letter c as complement.

    From this I figure I need to find the following probabilities:

    P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.

    So, how do I do this? I'm kind of confused at this point. I'm sure I have to draw a table.. but I'm not sure how.. please, if you can.. help me.

    #2. Given the following probabilities, draw a probability tree to compute the joint probabilities.

    P(A)= .8
    P(BlA)= .3
    P(Ac)= .2
    P(BlAc)=.3

    Again..I feel that I need to find the probabilities of the following for the tree:

    P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.


    #3. I'll get to this later. I would like some help with the first two problems. I"m not sure were to go with those. Thanks!
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  2. #2
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    Hello,


    I'm sitting here confused. I made up a chart.. but I'm almost certain it is not correct. However, I'm thinking now that I do not have to make a chart for this problem.

    Problem #1. The joint probability for P(A) = .8 given the rest of the Probabilities in that problem is .32 since P(A)*P(BofA)=.32? Not sure.. but I think I'm right about that one.

    Wouldn't the probability of P(BofA)=.32 also since it is also using the multiplication rule?

    I'm not sure what to do with the complements.


    Thanks!
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  3. #3
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    What does P(BofA) mean?
    I have never seen that notation.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by statsaway View Post
    Hello,


    This is my first post here. I'm in need of some help understanding these three problems.

    #1. Determine all joint probabilities from the following.

    P(A)= .8
    P(BlA)= .4
    P(Ac)= .2
    P(BlAc)=.7

    read the letter c as complement.

    From this I figure I need to find the following probabilities:

    P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.

    So, how do I do this? I'm kind of confused at this point. I'm sure I have to draw a table.. but I'm not sure how.. please, if you can.. help me.

    #2. Given the following probabilities, draw a probability tree to compute the joint probabilities.

    P(A)= .8
    P(BlA)= .3
    P(Ac)= .2
    P(BlAc)=.3

    Again..I feel that I need to find the probabilities of the following for the tree:

    P(A and B), P(A and Bc), P(Ac and B), and P(Ac and B). The c's should be read as complement.
    use the formula for conditional probability.

    Recall, that if P(F)>0, we have:

    P(E|F) = \frac {P(E \cap F)}{P(F)}

    so, for instance, to find P(A \cap B):

    P(B|A) = \frac {P(A \cap B)}{P(A)}

    \Rightarrow P(A \cap B) = P(B|A) \cdot P(A)

    and just plug in the values you were given
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  5. #5
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    Quote Originally Posted by Plato View Post
    What does P(BofA) mean?
    I have never seen that notation.

    I can't figure out how to type in some math notations. So, I meant it to look like this:

    P(BlA) It's a straight up and down line.. I used an Lowercase L instead .. and of instead of the line also.... sorry about the confusion.

    Thanks
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  6. #6
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    Quote Originally Posted by Jhevon View Post
    use the formula for conditional probability.

    Recall, that if P(F)>0, we have:

    P(E|F) = \frac {P(E \cap F)}{P(F)}

    so, for instance, to find P(A \cap B):

    P(B|A) = \frac {P(A \cap B)}{P(A)}

    \Rightarrow P(A \cap B) = P(B|A) \cdot P(A)

    and just plug in the values you were given

    Hmm.. we have not learned conditional probability formula yet. So, I can't necessarily use that to formulate my answers.

    I'll tell you what I have to go by. In this section we learned about the Complement rule, Multiplication rule, multiplication rule for independent events, Addition rule, Addition rule for Mutuallly Exclusive Events.

    Before that we learned Intersection of points, conditional probability, independent events, Union of Events A and B.

    thanks for your reply.. I really appreciate that.. I will use it in the future.. i'm sure.. but I would like to know how to solve these problems w/o that. This is just basic statistics.. and we are only on chapter 6, just now learning about probability.

    Thanks!
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  7. #7
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    Ok, assuming I'm using that conditional prob. formula above.. I'm still looking for Joint probabilities. I already know P(BlA)= .4.. that is given along with P(A)= .5


    thanks
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  8. #8
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    This will help you with the first problem.
    P(B^c |A) = 1 - P(B|A)
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  9. #9
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    Quote Originally Posted by Plato View Post
    This will help you with the first problem.
    P(B^c |A) = 1 - P(B|A)

    THanks.. that helped.. we really struggled over those two problems only to find out there were examples in the book ( Baye's Law!) AFTER the problems were given in the next section. Anyway, we figured them out.. But, I have a problem figuring out this next problem about diversity indexes.

    #3. In early 2001, the United States Census Bureau started releasing the results of the latest census. Among many other pieces of information, the bureau recorded the race or ethnicity of the residents of every county in every state. From the results the bureau calculated a diversity index,"which measures the probability that two people chosen at random are of different races or ethnicities. The census determined that in a county in Wisconsin 80% of its residents are White, 15% are Black, and 5% are Asian. Calculate the diversity index for this county.

    * ok, looking thought the book, even after the question.. there is nothing about diversity index anywhere. Can someone guide us on were to start with this problem.. it's the last one we have to figure out.


    Thanks!!!!!
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