Probability that two non-twin siblings are born on same day

Question

I want to compute this probability. I take the first sibling, mark their birthday, and then assume that the second siblings birthday is random, so I get that there is a 1/365 chance. Certainly there are many factors I have not taken account for.

Upon googling this, this article, says that "UC Berkeley’s Michael Hutchings calculates the probability at a little less than one in 500,000 for a family with two children who aren’t twins."

This seems radically different from my estimation. Can anyone rectify this?

Answer 1

The odds you mentioned are for being born on the same day at the same time. Assuming a precision of 1 minute, this will be $\frac{1}{24\times 365 \times 60} \approx \frac{1}{500000}$ like the article mentions. Without any further data, the best guess towards your question is $\frac{1}{365}$

Answer 2

The simplest model assumes that there are 365 days in a year, each sibling having the same probability of 1/365 of being born on any of those days, and their births are independent. That implies the probability that they have the same birthday is 1/365.

You can make improvements on this model is various ways. For example, you can include leap days. For that model you'd probably want to assume that the probability of being born on Feb 29 is 1/4 the probability of being born on any other day. It complicates the computations a bit, and leads to a slightly lower probability for an answer.

You could also get a table of the frequencies for births on each of the days of the year and weight the probabilities for each day to be proportional to those frequencies. I don't know what answer that gives, but I suspect it would be slightly greater than 1/365.

Finally, you could get some data on births of children in the same family. You would find that they often occur in the same season, and even in the same month. That means that the birthdays of siblings are not independent. You might find that the probability of being born on the same day is 1/200 or higher.