Chances of a Charter School

How do I calculate the probability of getting into at least 1 charter school?  I can figure out the chances of getting into each school individually, but in considering my school choice it would be helpful to know what my chances are of getting into ANY of the charter schools to which I am applying.  I’m no statistics expert, but I was pretty good in math 20 years ago, and I know that I can’t just add up the acceptance percentages of the schools.  Get out your slide rules people!

I consulted with a statistician friend of mine, and here is the formula that she shared.

    [box]1 – (probability of getting REJECTED by all the schools)[/box]

To get the probability of getting rejected (where rejection=100-acceptance) by all the schools you have to multiply all of the rejection rates together.  So the formula ultimately looks like this.

    [box]1 – (rejectionrate1 * rejectionrate2 * rejectionrate3 * etc…)[/box]

I will use my situation as an example.  I am applying to 4 charter schools whose acceptances are all by lottery.  I was already denied a seat at one charter already, but let’s leave that fact alone for the sake of simplicity.  Their acceptances by lottery give us a chance of 10%, 10%, 15%, and 15% respectively.  Each lottery is run independently and my results in one lottery have no bearing on the other lotteries.

In my case of acceptance rates (10%, 10%, 15%, 15%), I would do the following:

    [box]90% * 90% * 85% *85% = 58.5%
    (otherwise represented as .90 * .90 * .85 * .85 = .585)
    [/box]

This is the probability of not being selected in any charter school lottery.

So applying the rest of the formula, you have to subtract that value from 1.

    [box]1 – (probability of getting rejected by all the schools): 1.00-.58 = .415 (or 41.5%)[/box]

This means that my son has a greater chance a not getting into any school (58.5%) then he has of getting into at least 1 (41.5%).

Maybe I would be happier if I had stayed ignorant.

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