Help with simple probabilities problem?

#1
Hi guys,

I'm having trouble finding a satisfactory answer to this one: what is the probability that, in a group of 7 people, you will find the coincidence that 4 of them are born in the second half of May? I would have thought it's (1/24)^4, since the total number of people in the group should not matter, but only how many of them are born in that time of the year

Thanks for any help!
 

Dason

Ambassador to the humans
#3
since the total number of people in the group should not matter, but only how many of them are born in that time of the year
What makes you think the size of the group shouldn't matter? Doesn't it make a difference if the group size is: 1, 4, or 100000000?

I mean I wouldn't find it that surprising it in a group of 100000000 at least 4 people had birthdays in the last half of May. In a group of 1 I would find this very surprising (impossible even!). In a group of 4 it would seem quite surprising but at least possible.
 
#4
My reasoning was that the more people you place this condition on (being born in the second part of May), the more that probability will go down, and that you don't have to take into account the size of any group that these people may be a part of, but I see what you mean about this coincidence being less surprising in a large group.

So then I guess the probability is in fact (1/24)^4 * (23/24)^3?