# Thread: calculate probability of student retention

1. ## 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%).

2. Hello, jlamp!

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

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

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

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

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

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

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

. . . . . . . . $\displaystyle =\;0.561910874...$

. . . . . . . . $\displaystyle \approx\;56.2\%$

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