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Math Help - calculate probability of student retention

  1. #1
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    calculate probability of student retention

    Hi, I have a table containing grade levels K-5 with 5 different years as col/row headers and retention % as data fields. I want to track the K class through the 5 years and see what the probability is that a student went through all 5 years without being retained. We can assume that the class sizes remain constant for each year. Right now here are the datapoints I am looking at.....

    Kinder 2001-02 4.7%
    1st 2002-03 11.6%
    2nd 2003-04 5.6%
    3rd 2004-05 19.8%
    4th 2005-06 11.9%

    What are the chances a student went through all those years without being retained? I have tried a few things but am not confident with the resulting numbers...(~56%).

    Thanks for any help you can provide!
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, jlamp!

    The table contains: grade levels K-5 for five years, and retention %.

    . . \begin{array}{|c|c|c|}<br />
\text{Grade} & \text{Years} & \text{\% retention} \\ \hline <br />
\text{Kinder}& \text{ 2001-02} & 4.7\% \\<br />
\text{1st} & \text{2002-03} &  11.6\% \\<br />
\text{2nd} & \text{2003-04} & 5.6\% \\<br />
\text{3rd} & \text{2004-05} & 19.8\% \\<br />
\text{4th} & \text{2005-06} & 11.9\%\\ \hline<br />
\end{array}

    What is the probability that a student went through the five years
    without being retained?

    If (big IF) I understand the probolem, we have:


    . . \begin{array}{|c|c|}<br />
\text{Grade} & P(\text{not retained}) \\ \hline<br />
\text{Kinder} & 0.953 \\ \text{1st} & 0.884 \\ \text{2nd} & 0.944 <br />
\\ \text{3rd} & 0.802 \\ \text{4th} & 0.881 \\ \hline \end{array}



    P(\text{not retained for the 5 years})

    . . . . . . . . =\;(0.953)(0.884)(0.944)(0.802)(0.881)

    . . . . . . . . =\;0.561910874...

    . . . . . . . . \approx\;56.2\%

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  3. #3
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    Jul 2010
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    That is what I got but wasnt sure on the method. Thanks for your help
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