|
|
|
|
|
|
by EGreg
2561 days ago
|
|
|
Assuming a uniform distribution, the probability is 1/365 for any person#. Those probabilities add up linearly if the people are guaranteed to have different birthdays (union/OR). Otherwise the probability of NOT having someone with the same birthday goes down exponentially as a an exponential power of the fraction 364/365 (intersection of complement/AND NOT) It’s exactly what you would expect from classical combinatorics with cards with or without replacement. Your term “confident” is vague. I produced a series called Thinking Mathematically on youtube that makes all of this and other related topics clear for anyone... I recommend checking it out! https://m.youtube.com/channel/UCuge8p-oYsKSU0rDMy7jJlA And here are the notes for it http://magarshak.com/math/numbers.pdf http://magarshak.com/math/sets.pdf http://magarshak.com/math/logic.pdf # if we exclude all people born leap years |
|
|
Why would we assume a uniform distribution of birthdays? For example, birthdays occurring on the 31st of a month are probably less likely to occur on average given that every month does not have 31 days. This is just one example and doesn't even go into seasonality of conception cycles.