Abhi077 wrote:

If there are a certain number of students in a classroom, 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 classroom.

As this is a DS question, all we need to do is figure out if we could calculate the answer should we want to.

Especially in questions like this, where actual calculation is complicated, it helps to keep this in mind.

In particular, we need to calculate "the number of ways to pick birthdays for students so that at least 3 students have birthdays in the same month" and divide it by "the total number of ways to pick birthdays for students". Since we know the number of months/days in a year, and assuming birthdays are evenly distributed, all we really need to know to calculate is the total number of students.

This is what we'll look for and is a Logical approach to solution.

As (1) does not give us the total number of students and (2) does, (2) is sufficient.

(B) is our answer.

If this sort of logic is confusing for you, you can instead try small numbers to help make things more concrete.

This is an Alternative approach.

(1) Say we have only 2 students or only 1 student in the classroom. Then the probability of having 3 together is 0. On the other hand, say we have 100, or 500, or some other really large number of students. Then the probability is definitely positive, meaning different from 0.

Insufficient.

(2) Say we take our 25 students and put them into different months. Since putting 2 students in every month uses up only 2*12=24 students, then the next student must be assigned to a month that already has 2 students in it. Therefore we are guaranteed to have at least one month with 3 students' birthdays and our probability is 1.

Sufficient.

(For those interested, the logic in (2) is called the 'pigeonhole principle'.)

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