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There are 27 students on the collage debate team. What is the probabil

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There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 20 Oct 2010, 06:57
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There are 27 students on the collage debate team. What is the probability that at least 3 of them have their birthdays in the same month?

A. 0
B. 3/27
C. 3/12
D. 1/2
E. 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Oct 2014, 03:22, edited 1 time in total.
Renamed the topic and edited the question.
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Re: There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 20 Oct 2010, 09:14
worst case
--------------
even distribution of 27 students' birth months across 12 months..
after 24 students, each month will have 2 students' birthday. The rest 3 students' birthday can go in to any month
making the count to 3 or more.

So this is always true or the situtaion will exists all the time and hence the probability should be 1 (E)

(put little more description)
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Re: There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 17 Mar 2017, 13:34
It is not 1, but some value very close to 1. Is this a valid question? Should there be an "approximate" in the question?
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Re: There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 18 Mar 2017, 01:26
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Re: There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 18 Mar 2017, 03:37
krushna wrote:
worst case
--------------
even distribution of 27 students' birth months across 12 months..
after 24 students, each month will have 2 students' birthday. The rest 3 students' birthday can go in to any month
making the count to 3 or more.

So this is always true or the situtaion will exists all the time and hence the probability should be 1 (E)

(put little more description)


Sure, correct answer. I think we don't need much calculation for this question, just simple logic right?

Similar simple logic question :
In a drawer which contain 23 pcs red socks and 15 pcs white socks, how many minimum socks should we take without looking to get one pair with the same color?
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Re: There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 18 Mar 2017, 19:28
Bunuel wrote:
manhasnoname wrote:
It is not 1, but some value very close to 1. Is this a valid question? Should there be an "approximate" in the question?


Why do you think that the probability is not 1? It's not clear at all from your post.


Sorry. I was doing that by numbers. I totally missed the logic part.

Even if I use numbers, I should arrive at probability of 1. I screwed up caclulation somewhere. It is not worth discussing anymore. My bad. Sorry again.
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Re: There are 27 students on the collage debate team. What is the probabil [#permalink]

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New post 11 Jan 2018, 15:35
Hi All,

This prompt is more a 'logic' problem than a math question. We have 27 students and 12 potential months in which those 27 students could possibly have their birthdays. It's possible that all 27 birthdays are in the same month or that the birthdays are "spread out" over the 12 months. We're asked for the probability that at least 3 of the birthdays are in the SAME month. Note that the prompt doesn't specify which month - so ANY month will do.

It might help to think in terms of how you might avoid having at least 3 birthdays in the same month. To do that, you would have no more than 2 birthdays per month. Over the course of 12 months, you could place (12)(2) = 24 of the birthdays and not have 3 or more in any given month. However, we have to place 27 birthdays - and if each of the 12 months already has 2 birthdays, then wherever you put those remaining 3 birthdays... there WILL be at least one month that includes at least 3 birthdays. Thus the probability of this outcome is 100% = 1.

Final Answer:
[Reveal] Spoiler:
E


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Re: There are 27 students on the collage debate team. What is the probabil   [#permalink] 11 Jan 2018, 15:35
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