Re: Harder puzzles easier; 4 points in plane

CBFalconer said:

Phil Carmody wrote:
Richard Heathfield <rjh@xxxxxxxxxxxxxxx> writes:
CBFalconer said:
Phil Carmody wrote:

... snip ...

To make it harder still - add still more people:
What's the probability of 400 people (selected uniformly)
not sharing any birthday?

Zero.

Yes, unless you want to cheat by, say, re-interpreting the
question to include people's year of birth in the definition
of "birthday", in which case the problem really does become
significantly more difficult.

Well, everyone's assumed this takes place on planet earth too,
it would be a different answer on venus or mars!

And those pesky leap years could mess things up too.

Nope, leap years don't affect that answer in the least.

Since the question is "What's the probability of...", a correct answer is
an expression that resolves to a value in the range 0 to 1 exclusive, to
some reasonable degree of precision.

Assuming present-day Earth: chance of TWO people not sharing a birthday -
leap years excluded:

364/365

Assuming present-day Earth: chance of TWO people not sharing a birthday -
leap years included, with no bias against leap years in the distribution:

365/366

(If 29/2 birthdays are only 25% as common as other days, the answer is very
slightly different again.)

The values clearly differ even for two people. They will certainly differ
for four, and vary greatly for forty. I can, however, accept that the
answer for four hundred does remain the same.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999
.

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