smoothgrh
smoothgrh
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August 21st, 2019 at 8:58:29 PM permalink
Let's say 4 kids are together in one 3rd grade classroom. The school has 4 classrooms with 22 kids for 88 kids total in each grade.

If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)
RS
RS
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August 22nd, 2019 at 2:43:45 AM permalink
Quote: smoothgrh

Let's say 4 kids are together in one 3rd grade classroom. The school has 4 classrooms with 22 kids for 88 kids total in each grade.

If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)


Are we talking about a specific set of 4 kids or any 4 kids? Nevermind, that's a stupid question.

I would think the odds would be:

(3/21) * (2/20) * (1/19) = 0.00075187969 = 1-in-1330 odds.
ChesterDog
ChesterDog
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August 22nd, 2019 at 3:56:52 AM permalink
Quote: smoothgrh

Let's say 4 kids are together in one 3rd grade classroom. The school has 4 classrooms with 22 kids for 88 kids total in each grade.

If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)



I get approximately one in 79.7.

(21/87) * (20/86) * (19/85) = 266/21199

unJon
unJon
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August 22nd, 2019 at 5:52:32 AM permalink
Quote: RS

Are we talking about a specific set of 4 kids or any 4 kids? Nevermind, that's a stupid question.


Itís not a dumb question at all. Because it happens 100% of the time every year for some set of four kids. Itís impossible to sort 88 kids into 4 rooms without having at least 4 that end up together in consecutive years.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
kubikulann
kubikulann
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August 22nd, 2019 at 6:50:34 AM permalink
Quote: ChesterDog

I get approximately one in 79.7.

(21/87) * (20/86) * (19/85) = 266/21199

Thatís the correct answer.

(But What makes you think the school is distributing kids randomly? If they know their job, they would try to keep friends together ó and separate troublemakers.)
Reperiet qui quaesiverit
billryan
billryan
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August 22nd, 2019 at 8:09:41 AM permalink
Quote: kubikulann

Quote: ChesterDog

I get approximately one in 79.7.

(21/87) * (20/86) * (19/85) = 266/21199

Thatís the correct answer.

(But What makes you think the school is distributing kids randomly? If they know their job, they would try to keep friends together ó and separate troublemakers.)



If you separate the troublemakers, you'll have them in every classroom. Concentrate them and you have three good classes and one potential zoo.
If I was doing the assigning,I'd divide them strictly on academics. First class would be the best students who will not be held back by students not up to their pace.
If those four students want to stay together, all they have to do is excel and be in the first group.
7craps
7craps
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August 22nd, 2019 at 8:36:00 AM permalink
Quote: smoothgrh

If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)

about 1 chance in 80
probability is exactly: 266/21199
using pari/gp calculator
online here: https://pari.math.u-bordeaux.fr/gp.html
gp > a=4*(binomial(4,4)*binomial(84,18))/binomial(88,22);
gp > aDec=1.*a;
gp > a1chanceIn=1/aDec;
gp > a
%4 = 266/21199
gp > aDec
%5 = 0.012547761686872022265201188735317703665
gp > a1chanceIn
%6 = 79.695488721804511278195488721804511278

4*(binomial(4,4)*binomial(84,18))/binomial(88,22)
4 = there are 4 possible classrooms of equal size
binomial(4,4) = 4specificKidsChoose4
binomial(84,18) = 84otherKidsChoose18
binomial(88,22) = 88totalKidsChoose22

I used the hypergeometric probability solution as it is easily used for even more difficult type of questions like these. example: How about only 3 out of the 4 being in one classroom?

simulation shows this to be about correct
sum get lucky
Last edited by: 7craps on Aug 22, 2019
winsome johnny (not Win some johnny)
smoothgrh
smoothgrh
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August 22nd, 2019 at 9:19:00 AM permalink
Quote: kubikulann



(But What makes you think the school is distributing kids randomly? If they know their job, they would try to keep friends together ó and separate troublemakers.)



Thanks everyone! My son and his 3 friends all live close to each other, so it was a happy coincidence they were in the same class last year. They're all together again, so I thought "what are the odds???"

However, you're probably right that it's not random, even though that's what the secretaries saidóit's probably just the company line to say it's random. I'd agree with separating troublemakers!
Last edited by: smoothgrh on Aug 22, 2019

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