Dave
8th May 2003, 12:24
(Dont read this if you don't like a bit of Maths!)
I've been quite suprised to notice that someone has had a birthday everyday i've logged into this bulletin board. Which made me wonder what would the probability of two or more people having there birthday on the same day! (I hope theres space to put two names there, Jon!) I think you'll agree the result is quite suprising:
Now, For one person, there are 365 distinct possible birthdays.
Then, for two people, there is 364 birthdays she/he could have without matching the first's birthday.
If there is no match after two people, the third person has 363 different birthdays that do not match the other two. So, the probability of a match is 1 - [(365)x(364)x(363)]/[(365)x(365)x(365)].
So, The formula for calculating the probability of a match with n birthdays is 1 - [(365)(364)(363)...(365 - n + 1)]/(365)^n.
This looks a bit boring, but lets put in a number...
If 5 people use the B.B. the chance of two people having the same birthday is remote.
But if 25 use the B.B. The probability is OVER 50%
If 45 use the B.B. The probability is OVER 90%
If 100 of us use the B.B. the odds are more than three million to one on that two share a birthday!
I suspect any Gamblers amongst us could use this to win some money of unsuspecting friends!:eek:
Dave
I've been quite suprised to notice that someone has had a birthday everyday i've logged into this bulletin board. Which made me wonder what would the probability of two or more people having there birthday on the same day! (I hope theres space to put two names there, Jon!) I think you'll agree the result is quite suprising:
Now, For one person, there are 365 distinct possible birthdays.
Then, for two people, there is 364 birthdays she/he could have without matching the first's birthday.
If there is no match after two people, the third person has 363 different birthdays that do not match the other two. So, the probability of a match is 1 - [(365)x(364)x(363)]/[(365)x(365)x(365)].
So, The formula for calculating the probability of a match with n birthdays is 1 - [(365)(364)(363)...(365 - n + 1)]/(365)^n.
This looks a bit boring, but lets put in a number...
If 5 people use the B.B. the chance of two people having the same birthday is remote.
But if 25 use the B.B. The probability is OVER 50%
If 45 use the B.B. The probability is OVER 90%
If 100 of us use the B.B. the odds are more than three million to one on that two share a birthday!
I suspect any Gamblers amongst us could use this to win some money of unsuspecting friends!:eek:
Dave