I'm doing some research for a project I'm working on
and I am looking for insight.
OK, back to trying to help. Let's make some assumptions about families. Let's say the group of people you are considering has 8 people (parents, two children, two sets of grandparents). The probability of two having the same birthday (as shown in an earlier post) is:
1 - 365! / (365-8)! / 365^8 = 7.3%
That means that you would expect one out of every 14 families on average to have common birthdays. You should be able to go around the room in your class and find people who have common birthdays in their families. That doesn't mean that they will share that common birthday, only that there is a shared on in their family. If you extend the group out to aunts, uncles, cousins, etc. there will be lots of matches. Between 10 and 30 people, the probability of a match goes up by around 3% per person added. As noted earlier, 23 people is around the 50% point. If we assume the typically family has two children, then grandparents (4), uncles and aunts (4), cousins (4), parents (2), sibling (1) and you add up to 20 and a 41% common birthday probability. Basically, you aren't going to find any lack of families with births in common.