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Math Help - Bayes' Formula .. Please Help

  1. #1
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    Exclamation Bayes' Formula .. Please Help

    1. Using this table:

    Down Payment 5% 10% 20% 25%

    # of Mortgages
    with this down 1260 700 560 280
    Payment

    Probability of .05 .03 .02 .01
    Default

    ?: A bank finds that the relationship between mortgage defaults and the size of the down payment is given by the above table. If a default occurs, what is the probability that it is on a mortgage with a 5% down payment? Use Bayes' Formula and a tree diagram Show work

    (The thing is i have to answer these questions with a tree diagram and bayes' formula and i have show calculations. for example question 1. should show a tree diagram; the left part of the tree should have four branches (one for each of the four levels of down-payment). Each of these four branches should then sprout two branches- one for default and the other for no default. Each branch should be labeled with its probability.)

    2. This table shows the percent of U.S. households in each region and the percent per region using central air conditioning.

    Northeast Midwest south west
    Region 19.4 23.7 35.2 21.5

    Uses Central AC 22.1 51.3 69.4 26.9

    Find the probability that a household using central air conditioning is in the midwest? Use a tree diagram and bayes' formula show work!

    3. The table gives the proportions of people over age 20 in the U.S. population, and the proportions of those that live alone, in a recent year.

    Age Proportion in Population age 20 or higher Proportion living alone 20-34 .293 .088
    35-54 .412 .107
    55-74 .212 .191
    75 and older .083 .393


    Find the probability that a randomly selected person age 20 or older who lives alone is age 75 or older. Use tree diagram and bayes' formula show work!

    Please help I'm really confused with the whole tree diagram and bayes' formula thing.. if anyone could answer these that would be great..Thanks again!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lizzi583 View Post
    1. Using this table:

    Down Payment 5% 10% 20% 25%

    # of Mortgages
    with this down 1260 700 560 280
    Payment

    Probability of .05 .03 .02 .01
    Default

    ?: A bank finds that the relationship between mortgage defaults and the size of the down payment is given by the above table. If a default occurs, what is the probability that it is on a mortgage with a 5% down payment? Use Bayes' Formula and a tree diagram Show work

    (The thing is i have to answer these questions with a tree diagram and bayes' formula and i have show calculations. for example question 1. should show a tree diagram; the left part of the tree should have four branches (one for each of the four levels of down-payment). Each of these four branches should then sprout two branches- one for default and the other for no default. Each branch should be labeled with its probability.)
    Well the contingency tree should look like that in the attachment.

    RonL
    Attached Thumbnails Attached Thumbnails Bayes' Formula .. Please Help-gash.jpg  
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  3. #3
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    Thanks a bunch anyone have any other input on the questions.. I just can't figure these out! Thanks
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by lizzi583 View Post
    1. Using this table:

    Down Payment 5% 10% 20% 25%

    # of Mortgages
    with this down 1260 700 560 280
    Payment

    Probability of .05 .03 .02 .01
    Default

    ?: A bank finds that the relationship between mortgage defaults and the size of the down payment is given by the above table. If a default occurs, what is the probability that it is on a mortgage with a 5% down payment? Use Bayes' Formula and a tree diagram Show work
    Bayes' theorem tells us that:

    p(5\%~ down|dfault)=\frac{p(dfault|5\% ~down)p(5\% ~down)}{p(dfault)}

    Now from the tree diagram we can see that (this is the sum of the default probabilities on the right):

    p(dfault)=0.0225+0.0075+0.004+0.001=0.035

    also:

    p(dfault|5\%~down)=0.05

    p(5\%~down)=0.45

    form which you can find p(5\%~ down|dfault)

    RonL
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    Thanks so much!! Can anyone help me with questions 2 and 3??? thanks again!
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by lizzi583 View Post
    Thanks so much!! Can anyone help me with questions 2 and 3??? thanks again!
    You now have an example, so you should at least make an attempt at the next question yourself, then come back with specific problems that you are having if you need further help.

    RonL
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