Dating someone with the same birthday
It’s like if I had a 1/10 chance of winning the lottery and I meet another person who also has a 1/10 chance of winning the lottery, then combined we have a 2/10 chance of winning the lottery.
The odds of a “coincidence” increases with each person: Me meeting a person with the same birthday: 1/365 Me and one other friend meeting someone with the same birthday: 1/(365/2) = 183 Three of us meeting someone with the same birthday: 1/(365/3) = 1/122 …
But P(same day) should be roughly independent of whether you were born in the same year.
So it will be $\approx$ P(Same year) $\times$ P(Same day).
Twenty nine of us meeting someone with the same birthday: 1/12.
One person has a 1/365 chance of meeting someone with the same birthday.Two people have a 1/183 chance of meeting someone with the same birthday. Those two people might also have the same birthday, right, so you have to add odds of 1/365 for that.The odds become 1/365 1/182.5 = 0.008, or .8 percent.A consequence of this is that the pool of people you know from the exact same ages is by guesstimation a factor of 5 bigger than the expected value, if $age If it's an event specified before the fact, you can simply break it down: The chance that your boyfriend was born the same year as you is actually very high (especially given many situations tend to bring people of very similar age together); it's a very difficult probability to calculate, though, without data.If you had that probability, P(Same day and same year) = P(Same year) $\times$ P(Same day|same year).