What is the probability of not being born on a Friday the 13th?

Answer 1

This question appears simple but it is not.

The simplistic approach goes as follows:

1. There are twelve 13ths in a year of 365 days (but what about Leap Years?).
   
2. Each 13th can fall on any day of the week so, on average, there will be 12/7 Fridays in a year.
3. That leaves 365 - 12/7 = 363 2/7 days which are not Friday the 13 and so the probability is 363 2/7 / 365 = 0.9953, approx.

But at step 1 you have ignored Leap Years. At step 2 you assume that the day of the week for the 13th is independent from one month to another. This is not true: for example, in a non Leap Year, February and March must be the same. In fact. in the 20th Century, the 13th fell on Fridays more than any other day of the week. However, it is possible, though tedious, to adjust for both these factors but there are others which make the task virtually impossible:

Births are not uniformly distributed across the year. In the UK, for example, in the 36 years from 1979 and 2014 (inclusive), the 13th did not feature in any year as the most popular date of birth. With only 34 years that is not too extreme. However, if the date was approximately evenly distributed, you would expect the most popular day to lie in the range 10-16 around 8 times in 34 years. In fact, this happened only once!

The most popular day to be born was Friday, followed very closely by Thursday, Wednesday, and Tuesday. Mondays tended to have fewer births than other weekdays. Saturdays and Sundays have even fewer births. The lower figures for the weekends may be due to management decisions not to schedule planned births, such as caesarean sections at weekends when fewer staff are available. This may have a bunching effect of Fridays.

So you are faced with 13 being less common but Fridays being more so. Disentangling that requires some very serious data crunching!