There are 12 students. Compute the probability that at least 3 students are born in the same month.

Am I right with:

OR

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- Apr 19th 2008, 09:20 AM #1

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- Apr 19th 2008, 10:00 AM #2

- Apr 19th 2008, 10:13 AM #3

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Thanks!

But actually, why does Pr(at least 3 students are born in the same month) = 1 - Pr(exactly 2 people are born in the same month) ?

1 - Pr(exactly 2 people are born in the same month) can still have other cases besides having at least 3 students born in the same month right?

Pls advise! ^_^

- Apr 19th 2008, 11:44 AM #4
Please look at the webpage: Birthday Problem -- from Wolfram MathWorld

You will see that this is far from an easy problem.

P.S. For this problem n=12 & d=12.

- Apr 19th 2008, 09:42 PM #5

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I guess I should reduce the numbers a little.

Say the question now is:

There are 5 students. Compute the probability that AT LEAST 2 students are born in the same month.

I will take:

Pr(AT LEAST 2 students born in same month) = 1 - Pr(NONE of them born in same month)

which is

1 - (12_P_5 / 12^5)

Please tell me I am correct =P