Two Brains

[belanna]

How many spectators have to be at a football match to make it more likely than not that 2 people in the stadium will share the same birthday?

Answer given as none. The answer is 23 (which equals both teams plus ref.)
How is 23 the answer when there are 365 possible birthdays?

[bibblebub]

take any one person

add a 2nd person; the chance neither has the same birthday = 364/365 (assume non-leap year)

add a 3rd person; the chance that none have the same birthday = = 364/365 X 363/365

add a 4th person; the chance that none have the same birthday = = 364/365 X 363/365 X 362/365

and so on

it's when you get to the 23rd person that that fraction (from all the multiplications) gets below 1/2 i.e. they are less likely to all have different birthdays than at least two of them sharing the same date

[bibblebub]

for the 3nd when i said "the chance neither has the same birthday" I should have put "the chance that they have different birthdays"

[bibblebub]

sorry again that ^ should have been for the 2nd

i'll give up here because typos are coming thick and fast

[belanna]

Thanks Bibblebub. I give up too.
I should have known the maths would be beyond me!

[bibblebub]

sorry I couldn't provide a clearer explanation, it's not that difficult