I am wondering how one would go about solving a problem such as this.(adsbygoogle = window.adsbygoogle || []).push({});

Lets say all schools compete in a competition where students are awarded a score from 0 to 5. It has been shown that the chances of a student receiving a 5 are 10%, a 4, 20% and a 3 are 25%, and below a 3 are 45%

Each school may have a different number of competitors as this is an individual event. One particular school has 7 competitors. 3 get a 5, 3 get a 4 and 1 gets a 3.

This school wants to be able to say that only 1 in x did as well.

I am thinking that if I mulitplied .10 *.10*.10*.20*.20*.20*.25 = .000002 or 1 in 500,000, but that is way too high because that is just the odds of the school getting that exact score.

I am also thinking that since the probability of getting below a 3 are 45% then if I looked at (1 -.45)^7 this is the probability of a school with 7 kids all doing better than threes (which we have in this case) so that works out to 1 in roughly 65 schools.

But this now is too low as this particular school did better than say a school that had 7 kids getting just 3's.

So assume that if a school has just one kid that gets a 4, this is better than a school that gets all 3's. and if another school has just 1 5 this is better than a school that has all 4's.

Ahh, my head is hurting now, please help me solve this problem correctly.

Thanks

-dif

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# Statistics and odds

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