What's the probability of two or more people in a group of 24, have the same date of birth?

Answer 1

Let's first figure out the probability that nobody has the same birthday.

Person 1 can have whatever birthday he/she wants.

The probability Person 2 doesn't have the same birthday as Person 1 is (364/365).

If the first two people have different birthdays, then the probability Person 3 doesn't have the same birthday as Persons 1 and 2 is (363/365).

If the first three people have different birthdays, then the probability Person 4 doesn't have the same birthday as Person 1, 2, or 3 is 362/365.

Continuing in this way, we find that the probability the first 24 people have different birthdays is

(364/365) x (363/365) x (362/365) x ... x (341/365).

If you multiply this out, you get that the probability no two people in your group of 24 have the same birthday is about 43.13%.

So the probability that at least two people have the same birthday is 56.87%.

(This probability first surpasses one-half at 23 people, and then rapidly gets closer and closer to 100%.)

Answer 2

Walter is off the mark.

Here's how it's done:

The number of ways to form a sequence for k people subject to the restriction that all k birthdays must be different is the permutation:

365Pk

The total number of sequences is 365^k

the ratio is the probability that all the birthdays are different.

so P(at least two with the same birthday)= 1-365Pk/365^k

Here's a table:

k, P(at least two with same birthday)
---------------------
22, 0.476
23, 0.507
40, 0.891
50, 0.970
70, 0.999

Among our first 40 presidents, two did have the same birthday:
Harding and Polk, Nov 2.

The table values are actually slight underestimates because birthdays are not uniform over the year. It has been proven that any deviation from the equally likely will increase these probabilities.

Answer 3

The probability of an individual having a paticular birth date is 1/365. So the probability of two people having the same birthdate is (1/365)^^2. The probability of two people having the same birthdate in a group of 24 is the probability of any two people having the same birthdate times the number of pairs of people in a group of 24. So the chance of two people having the same birthday in a group of 24 is 24*23/365/365 = 0.4%

Answer 4

Depends if u also want the year of birth.. if not 24/2=12 12*365= 4380 so the chances are 1 in 4380 for the same day of birth if they are all born in the same year I do believe..

Answer 5

Slightly more than 50 percent.