- #1

red65

- 13

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There are k people in a room. Assume each person’s birthday is equally likely to be any of the 365 days of the year (we exclude February 29), and that people’s birthdays are independent (we assume there are no twins in the room). What is the probability that two people in the group

have the same birthday?

say that we have 23 people, my approach is to calculate the number of pairs in the group which is 23 choose 2 then multiply these by the probability that 2 people have the same birthday which is 1/356(because the first pick any day from 365 days then the second has a probability of 1/365 of picking the same day )

why my approach is wrong?

thanks.