I want to know if you know how to calculate the percentage of being correct guessing someone’s birthdate. However, I want the answer out to 4 decimal places when in percent form.
Here is how:
You maybe inclined to say it is 100*1/365. This answer is correct out to 3 decimal places, even though you aren’t incorporating leap day. However, to get out to 4 decimal places we need to be more precise with leap day:
100*4/(365+365+365+366).
The reason for the 4 is because out of 4 different years you would get 4 guesses.
Or 100*1/365.25, where 365.25 is the average number of days in the year.
So the answer is, with leap day included:
Rather than:
Which doesn’t include leap day.
So, leap day accounts for 0.0002% of your answer out to 4 decimal places.
Logically, my next question now is:
If you have a leap day birthday, how much more likely are you to ask others to guess your birthday?
I would argue it is better to know, not the date that most people are born on, but the birthdate that makes people want to ask others to guess their birthdates.
You can bet that if someone asks me to guess their birthdate, that I would guess leap day. If someone reads this and asks me to guess, I don’t think their birthdate World be on leap day.
Now, another question I have is this. Someone I need to count on my knuckles know how many days there are in a particular month – just to make sure. If someone guessing a birthdate randomly chooses a month that they would normally want to double check how many days there are in that month, then I would bet they aren’t going to choose 31. For this same reason, the probability of getting dates that have the day on the 31st, would be a function of the guesser’s age.
Someone may guess dates that don’t exist. So when guessing birthdates, the average number of days in a year would arguably be more than 365.25.
So, I would bet the two main factors affecting whether you would guess a birthdate correctly are based on whether you were asked to guess or not (because they likely have a birthdate on leap day if they asked), and how old the guesser is (because it effectively changes the number of days of the year).