What is the probability somebody's birthday is the day before mine?

What is the probability that someone's birthday is the day before my birthday? For example, my birthday is Feb 28, what is the probability that my mom's birthday is Feb 27? Is it just $\frac1{365}$? That seems too simple to me but maybe I'm just complicating things unnecessarily.

Assuming a uniform distribution of birthdays throughout a 365-day year, and that "somebody" means "a fixed person chosen at random from the human population", $\frac1{365}$ is correct, since there is only one day that is immediately before a given day. If "somebody" is a person we can choose arbitrarily, the answer is $1$ since at least one person has been born on each day of the year, including 29 February.

In reality more people are born in the summer months, so the distribution of birthdays is variable and not at all uniform.

When considering 29 February as well as the usual 365 days in the first formulation of "somebody", the year also needs to be known in order to completely determine which day is "the day before my birthday". Once again, assume birthdays are uniformly distributed by day (not date). Since there are 97 leap years in the 400-year Gregorian cycle, the probability that a randomly chosen person has a specified birthday is $\frac{400}{400\cdot365+97}$ if that birthday is not 29 February and $\frac{97}{400\cdot365+97}$ otherwise.

If you want to make it hard:

There are $365$ choices her birthday (H) could be, and $365$ choices yours(Y) could be. So there are are $365^2$ pairs of birthdays (H,Y).

Of those $365^2$ pairs there are $365$ cases where $Y = H+1$. (Case 1: Y= Jan. 1-H=Dec 31. Case 2: Y= Jan. 2-H= Jan 1. Case 3: Y=Jan. 3-H= Jan. 2..... Case 365: Y= Dec. 31, H= Dec. 30$.

So the probability is $\frac {365}{365^2} = \frac 1{365}$.

If you want to do it the easy way.

There are $365$ days she could be born. The day before your birthday is precisely one of them and as likely as any other. So probability is $\frac 1{365}$.

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As for your birthday being Feb. 28.... No matter what your birthday is, the probability of her birthday being Feb. 27 is $\frac 1{365}$.

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Finally your title is "What is the probability somebody's birthday is the day before mine?"

The answer to that is 100%. There are tens of millions of people with birthdays the day before you.

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" That seems too simple to me" Why? Why should it be complicated?