What is the probability that there exists a day of the year such that exactly two out of the twenty people have their birthday on that day of the year

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lilac

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What is the probability that there exists a day of the year such that exactly two out of the twenty people have their birthday on that day of the year?

Is it nCr(20,2)*1/365^2*(364/365)^18 ?
 
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I'm not really sure whether its right or not I was just trying but I guess because there are 20 and and the probability that 2 share the exact birthday is something like that. I will appreciate if you have other ideas or if you can correct me.
 
lilac said:
I was just trying but I guess because there are 20 and and the probability that 2 share the exact birthday is something like that.
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Okay; now please *show* us the steps you used to obtain the expression that you posted. Thank you!

Eliz.
 
I'm here asking you guys cause I don't know like I'm not sure about this. So if anyone knows the correct answer somehow please share it. I will be thankful to you ?!
 
lilac said:
I'm here asking you guys cause I don't know like I'm not sure about this. So if anyone knows the correct answer somehow please share it. I will be thankful to you ?!
Click to expand...
Okay. We can help you be sure of your work and reasoning, but only once we know what they were. So please reply with a clear listing of your thoughts and steps, so we can see how you got your posted answer.

Thank you!

Eliz.
 
lilac said:
What is the probability that there exists a day of the year such that exactly two out of the twenty people have their birthday on that day of the year?

Is it nCr(20,2)*1/365^2*(364/365)^18 ?
Click to expand...
lilac said:
I'm not really sure whether its right or not I was just trying but I guess because there are 20 and and the probability that 2 share the exact birthday is something like that. I will appreciate if you have other ideas or if you can correct me.
Click to expand...
It appears that your thinking involves assuming this is a binomial distribution problem. What would be necessary for that to be true? How would you try to convince us that it is right?

If you decide that isn't really right, what other ideas do you have?

It seems to me that the wording is a little odd, perhaps in order to suggest a particular way to think about it. But it mostly confuses me. Is it considered a success if there are two such days, or if there is also another day that a group of three share as their birthday? It seems so; but that makes things harder. This is not the usual "at least two share a birthday" problem.

Also, the phrase "two out of the twenty" suggests something else has been said about the people. Please show us the entire problem, in context, in case that makes a difference.

And, again, please show details of your thinking, so we have something to talk about, beyond your wish to be told the answer.
 
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