True of False!?

Question

If you take 20 random people, the odds of two of them having the same birthday are 50%.

Answer 1

Actually this is based on truth.
It has become known as "The Birthday Paradox" although it is not technically a paradox.

The exact number is 23 people which results in a ~50.73% chance of having duplicate birthdays. (how this is derived can be found at my first source.)

For a more visual explanation see this graph:
http://en.wikipedia.org/wiki/Image:Birthday_paradox.png#file

See this in action at this virtual party:
http://projects.felipc.com/birthday-paradox/

Answer 2

False

Answer 3

False

Answer 4

False

Answer 5

False

Answer 6

False

Answer 7

False cuz there are 365 days in a year...and the odds of 2 having the same should be quite lower than 1/2.

Answer 8

I believe if you take 22 people, the odds are even higher (by a lot). It's 95% or something. This means the birthday itself, though, not always the year included. It's still strange, but true.

Answer 9

I'd have to go with False. There are 365 days in a year. The chances are 1 in about 150 chances of that happening.

Answer 10

By my calculations (done in a Microsoft Excel Spreadsheet)...

for 20 people the odds are about 58.86% that no two of them have the same birthday.

for 22 people the odds are about 52.43%, and
for 23 people the odds are about 49.27%

(I've disregarded the possibility of a Feb 29th birthday just to make the calculations simpler)