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If there are a certain number of students in a class, What is the prob

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If there are a certain number of students in a class, What is the prob  [#permalink]

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New post Updated on: 12 May 2018, 22:25
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If there are a certain number of students in a class room, What is the probability that at-least 3 of them have birthdays in the same month?

(1) There are no students born in the month of December.

(2) There are 25 students in the class room.

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Originally posted by Adi93 on 12 May 2018, 21:29.
Last edited by amanvermagmat on 12 May 2018, 22:25, edited 1 time in total.
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Re: If there are a certain number of students in a class, What is the prob  [#permalink]

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New post 12 May 2018, 21:47
Statement 1:
Since we don't know the number of students,
It is NOT SUFFICIENT.
Statement 2:
Let us assume each student is born in a separate month -- one in January, one in February... and so on.
You get that 12 students could have birthdays in separate months. But you have 25 students, which is obviously greater than 12. This means that at least two students share months of birth, since 25/12 = 2 remainder 1.
That covers 24 students: you've concluded that at least two students have the same month of birth. But since you have three students left, then they also have to be distributed in the 12 months of the year.
This means that one month of the year will have at least 3 students, which makes the probability you're looking for 1.
SUFFICIENT

Answer B

Adi93 wrote:
If there are a certain number of students in a class room, What is the probability that at-least 3 of them have birthdays in the same month?

(1).There are no students born in the month of December
(2).There are 25 students in the class room.

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Re: If there are a certain number of students in a class, What is the prob  [#permalink]

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New post 12 May 2018, 21:51
I) no student birthday in month of December
But I still don't know Number of students
If number of students is less than 10 and even if we assume that and distribute one student per month then one month would be without student
Other case could be that majority of students have birthday in same month
i.e 5 students birthday in one month etc

So both cases arises so insufficient

II)total students=25
We take extreme case assign one student each month and then evaluate means equal distribution
That case each month have 2 students i.e 12*2=24
Still one student Left
Which will go to any of month making count of 3 student birthday in that month
So we have at least one month which have at least three students

Other case- any month can have any number in such case at least 3 is already taken care of eg. all students in one month or 2 month or 5 month then each of month would have at least 3 birthday

So B is sufficient

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Re: If there are a certain number of students in a class, What is the prob &nbs [#permalink] 12 May 2018, 21:51
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