Originally posted by Mephisto2
I still find it very hard to follow the reasoning. Perhaps the problem is that you omit the possibilities of 3, 4, ... matching dates?
I'll move this to a much simpler problem..
When rolling two six sided dice you have to roll 18 times to
have a 50% chance to get a twelve. (right?)
Now assume the year has six days then there is a total of 21
( (5*6/2)+6 )
ways to combine two days since the combination 1 and 2 is the same as 2 and 1.
Out of these 21 combinations six are the same day twice (11 22 33 44 55 66) this means you would need to pick 21/6=3,5 to have a 50% chance to get at least one?
Back to orignal numbers:
If the dice has 366 sides. You would have to roll them 66978 times to have 50% chance of getting 732. (right?)
There are 366 results with the same day twice out of 67161 ((366*365)/2 +366) you need then 67161 /366 =183,5 to get 50%
and now magicaly I'm back at (19*20)/2=190
That is 20 people to get 50%.
And As I have said I KNOW this is wrong. But why?
Please I'm going Mad 🙂 And since I'm only examining pairs of dates 3 or more matching dates is not an issue.