Share The Same Birthday Math

It s only a paradox because our brains can t handle the compounding power of exponents.

Share the same birthday math. So the probability that at least two people share a birthday is 1 493 507 just greater than 1 2. What are the chances that with 6 people any of them celebrate their birthday in the same month. Put down the calculator and pitchfork i don t speak heresy. The first person could have any birthday p 365 365 1 and the second person could then have any of the other 364 birthdays p 364 365.

What is the probability that two people share the same birthday. 2 people is 11 12. The probability of being born any day of. The probability of no two people sharing the same birthday can be approximated by assuming that these events are independent and hence by multiplying their probability together.

If everyone was guaranteed to have a different birthday the answer would be lceil 365 2 rceil 183 365 2 183 note that this is not hard to obtain approximately using the taylor series approximation ln 1 x approx x ln 1 x x for small. This is the probability that all 23 people have a different birthday. 3 people is 11 12 10 12 4 people is 11 12 10 12 9 12 5 people is 11 12 10 12 9 12 8 12 6 people is 11 12 10 12 9 12 8 12 7 12. In a room of just 23 people there s a 50 50 chance of at least two people having the same birthday.

The probability of any two people not having the same birthday is 364 365. In a room containing n people there are n 2 n n 1 2 pairs of people i e. 365 2 365 2 because people in the room may share the same birthday. The birthday paradox is strange counter intuitive and completely true.

In a room of 75 there s a 99 9 chance of at least two people matching.