Question

In a room full of 30 people, what is the probability that at least 2 of them have the same birthday?

Answer 1

@ganeshie8 @dan815

Answer 2

day as in `monday, tuesday,... ` ?

Answer 3

as in day of the month

Answer 4

30 people where atleast 2 out of the 365 numbers common

Answer 5

what dan said

Answer 6

hold
i gota move my laptop first its over heating

Answer 7

so 1/1/1990 and 1/1/2000 are considered same birth days ?

Answer 8

yep

Answer 9

I can tell that it's more than 50% because I only take 23 people for that to happen

Answer 10

if you search birthday paradox you see how it's calculated. The idea is just to do 1 - P(no one share a same birthday)

Answer 11

it looks like a cool question to think about

Answer 12

the goal is to come to the answer without the internet

Answer 13

so you're saying find the prob that none of them share brithdays

Answer 14

yes, it's just
1 - (365/365) * (364/365) * (363/364) * .. all the way to the 30th person

Answer 15

typo
1 - (365/365) * (364/365) * (363/365) * .. all the way to the 30th person

Answer 16

\[\sum \limits_{k=2}^{30}\binom{30}{k} \left(\dfrac{1}{365}\right)^k \left(\dfrac{364}{365}\right)^{30-k}\]

Answer 17

i was thinking it was like that too but is there a closed form for this ganeshie

Answer 18

i feel like theres a nice function or something that gives the sum of that

Answer 19

its a binomial distribution right ?
p = 1/365
n = 30
k >= 2

Answer 20

yeah

Answer 21

true okay i get it!

Answer 22

we can integrate the normal distribution curve

Answer 23

yes thats the only simple way i guess ! we can approximate it by converting it to normal curve

Answer 24

ok cool

Answer 25

@geerky42 are you @usukidoll?

Answer 26

@dan815 you could also go back to a permutation by selecting 30 birthdays out of the 365 and assign them to the people which is 365p30 and then divide it by the total possible ways of assigning a birthday to someone?

Answer 27

that of course is the compliment event where everyone has a different birthday but we can subtract it from 1?

Answer 28

if no one share a same birthday, the complement of that is at least two people share a same birthday. So we subtract from 1. If fact, the formula is

Pr = 1 - (365Pn) / 365^n

in the case of 30, Pr = 70.6%

Answer 29

Yup ^

Answer 30

yes exactly i am curious as to how @ganeshie8 and @dan815 were going to solve it

Answer 31

Forget it, its not a direct binomial distribution - need to tweak some more >.<

Answer 32

No, I am not? @dan815

Answer 33

@dan815 I AM OVER HERE s t h u

Answer 34

@usukidoll :O