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Math Help - Terminology

  1. #1
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    Terminology

    Find the probability:

    In a rural area, given that the speed limit was no more than 40mph.

    \displaystyle\frac{\text{rural} \ \cap \ \leq 40\text{mph}}{\text{total}}

    Correct?
    Last edited by dwsmith; February 2nd 2011 at 05:30 PM.
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  2. #2
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    Please give the original problem statement. You haven't posted enough of the problem for us to figure it out.
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  3. #3
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    Quote Originally Posted by awkward View Post
    Please give the original problem statement. You haven't posted enough of the problem for us to figure it out.
    It is remarkable not much different than what you see now.

    What is the probability that it occurred:

    In a rural area, given that the speed limit was no more than 40mph?

    There is a chart as well but I am simplifying trying to figure out if that is saying rural intersect with under 40mph as the set in question.
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    Quote Originally Posted by dwsmith View Post
    It is remarkable not much different than what you see now.

    What is the probability that it occurred:

    [snip]
    What is "it"?
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  5. #5
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    Quote Originally Posted by awkward View Post
    What is "it"?
    Car accidents but that doesn't change anything.

    There is a chart of car accidents with numbers.
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  6. #6
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    OK, I'm going to stick my neck out and guess that your question is:

    What is the probability that a car accident will occur in a rural area, given that the speed limit is no more than 40 mph.

    Correct?

    It's hard to know how to answer this without knowing more about your chart. What does it look like?

    [edit]Changed "under" to "no more than" above.[/edit]
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  7. #7
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    Quote Originally Posted by awkward View Post
    OK, I'm going to stick my neck out and guess that your question is:

    What is the probability that a car accident will occur in a rural area, given that the speed limit is under 40 mph.

    Correct?

    It's hard to know how to answer this without knowing more about your chart. What does it look like?
    I dont need someone to tell me how to solve it. I am trying to figure out the set in question. Is that the intersection or union?

    \displaystyle\begin{bmatrix}\text{Accidents MPH}&\text{Rural}&\text{Urban}&\text{Total}\\ \leq 30&a&b&c \\ 30<A\leq 40&d&e&f \\ 40<A\leq 50&g&h&i \\ 55&j&k&l\\ \geq 60&m&n&o\\ \text{No Limit}&p&q&r\\ \text{Total}&s&t&u\end{bmatrix}

    Of course those are numbers not letters in the problem.
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    I'm still trying to guess your original question. OK, let's try again. I'm guessing the question is "If an accident occurs in an area where the speed limit is not more than 40 mph, what is the probability that it is in a rural area?"

    Proceeding symbolically, let

    R be the event that the accident occurs in a rural area and
    L be the event that the speed limit is less than or equal to 40 mph

    Then I think the probability you want is

    P(R | L) = \frac{P(R \cap L)}{P(L)}

    by the definition of conditional probability.

    Do you see how to find the numbers you need in your chart?

    [edit]It's getting late here, I'm going to have to sign off soon[/edit]
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  9. #9
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    Quote Originally Posted by awkward View Post
    I'm still trying to guess your original question. OK, let's try again. I'm guessing the question is "If an accident occurs in an area where the speed limit is not more than 40 mph, what is the probability that it is in a rural area?"

    Proceeding symbolically, let

    R be the event that the accident occurs in a rural area and
    L be the event that the speed limit is less than or equal to 40 mph

    Then I think the probability you want is

    P(R | L) = \frac{P(R \cap L)}{P(L)}

    by the definition of conditional probability.

    Do you see how to find the numbers you need in your chart?

    [edit]It's getting late here, I'm going to have to sign off soon[/edit]
    No guessing needed. This is the exact question verbatim.

    Quote Originally Posted by dwsmith View Post

    What is the probability that it occurred:

    In a rural area, given that the speed limit was no more than 40mph?
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  10. #10
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    I think there is something in your book just BEFORE the part you have quoted that sets the question up-- but in any case, I'm sticking with the interpretation that what you want is P(R|L), given the definitions of R and L in my previous post.
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  11. #11
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    Quote Originally Posted by awkward View Post
    I think there is something in your book just BEFORE the part you have quoted that sets the question up-- but in any case, I'm sticking with the interpretation that what you want is P(R|L), given the definitions of R and L in my previous post.
    Ok I will do conditional then.
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