What is the probability of being born in August?

Answer 1

Let me give you a simple answer first and two deep answers next.

Simple answer is, assuming that all months have the same number of days (which is very approximately true), 1/12.

If you want a slightly deeper answer, then 31/365 or 31/366 is correct, depending upon whether the year is a normal year or a leap year.

The correct answer, which might be argued as "philosophical", is as follows:

The Gregorian calender, the current standard calender in most of the world, adds a 29th day to February, 97 years out of 400, a closer approximation than once every four years. This would be implemented by making a leap year every year divisible by 4 unless that year is divisible by 100. If it is divisible by 100 it would only be a leap year if that year was also divisible by 400.So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800, and 1900 were not. In this millennium, 2100, 2200, 2300, 2500, 2600, 2700, 2900 and 3000 will not be leap years, but 2400 and 2800 will be. The years that are divisible by 100 but not 400 are known as "exceptional common years". By this rule, the average number of days per year will be 365 + 1/4 - 1/100 + 1/400 = 365.2425.In 400 years, thereforethere are 303 normal years and97 leap yearsTotal number of days in 303 years110,595 days(normal years)Total number of days in 97 years35,502 days(leap years)Total number of days146,097 daysTotal number of August months400(in 400 years)Total number of days in August in12,400400 yearsProbability that a person is 0.084875 or 1 in11.78202born in August (=12,400 / 146,097) or 31 in365.24251 / 12 =0.08333331 / 365 =0.08493231 / 366 =0.084699

There are assumptions in the above answer as well. These are

1. That all days in a year have the equal probability (which is not strictly true, as records of births will be required for verification)

2. The Gregorian calender has been in effect since 1700s. The probability as above will only work for years after the introduction of Gregorian calender.

Answer 2

not sure