can anyone help!!
We all know that the probability of finding two people in a room with the same birthday becomes better that a half when there are more than 23 people in the room. How many have to be in the room before the probability of two pairs of people with the same birthday is better than a half?
Hello sonia1Let's assume that the two pairs involve 4 different people; in other words, we are not allowing 3 people, A, B and C all to have the same birthday, and then forming pairs like (A, B), (A, C) and (B, C).
Then (as is well known - see the Wikipedia article in Mr F's post) the probability that in a group of people, at least two people share a birthday is given by:
, where is the number of permutations of chosen from 365,
Suppose now that in a room of people, a pair is found to have a common birthday. Then in the remaining people, the probability that there's at least one other pair with the same birthday is .
So the probability that both of these events occur is .
I have put the numbers into an Excel Spreadsheet - see attachment - using the PERMUT function to work out , and the answer comes out that with 31 people the probability is just under 0.5, and with 32 it's about 0.532.
I don't think it's any more complicated than that. Can anyone see a flaw in my reasoning?
Grandad