There are 23 people in a room. What is the probability that two people in the room will have the same birthday? Ignore February 29. @jim_thompson5910 @gan @phi @thomaster @hbh @dumbcow @Compassionate

Question

anonymous · Answer

Im not sure if this is correct but if there was one person in the room with them there would be a 1 in 365 chance of them having the same birthday. if their were 2 people in the room with one other person it would be a 2 in 365 chance. and so on. So for 23 people it will be a 22 in 365 chance for a pair of them to have the same birthday so 22/365 is 6%.....................Anyone else agree??????????

larseighner · Answer

If you knew the probability of NO two people in the room having the same birthday, you could subtract from 1.

larseighner · Answer

If NO two people in the room have the same birthday then the probability of 1 person in a room of 1 person not having the the same birthday as another person in the room is of course 1. No two people have the same birthday if there is only one person in the room.  So the first person's birthday can be any of 365 days out of 365 days.

Now a 2nd person into the room.  What are the chances of his birthday NOT matching that of person 1?