# Can anyone calculate these odd?

1. Nov 15, 2008

### kennyny11720

Hello Members,

Recently my boss introduced me to one of his friends at a golf outing. We then became friends and in time discovered how ironically some numbers between us are exactly the same. We are both born March 30th and thought that was amazing, only to realize that one of his children was born same day as my 1st child which is August 15th, then last but certainly not least his 2nd child is born same as my other child which is October 5th.

So the odds that I am trying to calculate is meeting someone with who is a father like me with same birth date and both children with same birth date. Please note none of the three dates were born in same year.

If anyone can come up with the odds and show me how I would apprediate it. And if you are that good (lol) then let me know odds of this. I have a third child, he does not, but if he had another child sometime in the future, what are the odds it would be same as my third child?

Thank you in advance!

Last edited by a moderator: Nov 15, 2008
2. Nov 15, 2008

### tiny-tim

Welcome to PF!

Hello kennyny11720! Welcome to PF!

Assuming that there is no reason to suspect a correlation, the chance of three pairs of birthdays being the same is 1/3653.

Allowing for the fact that the children's birthdays were in the wrong order, and that you'd be equally impressed if all three birthdays were "mixed up", the final figure is 6/3653, or about one in 8 million.

hmm … can anyone work out … if there are 1000 members of the golf club, what is the likelihood that at least one pair of members has that coincidence of birthdays?

(i know that in a group of 23 people, there's about a 50% chance of two people having the same birthday)

3. Nov 15, 2008

### BobG

Re: Welcome to PF!

Well, you really have to determine the probability that each member has at least 2 kids, as well, but, assuming they do:

There would be about a 1% chance of duplicating the original post's situation.

There would be about a 6% chance of having the same 3 birthdays, but possibly mixed up.

By time membership reaches 3350, the chances would reach about 50%.

Last edited: Nov 15, 2008
4. Nov 15, 2008

### BobG

As for calculating the chances, you have a 1/365 chance of having the same birthday as your partner. Your oldest a 1/365 chance, your second oldest a 1/365 chance, etc. Multiply the chances of each coincidence happening together. For the third child, you'd multiply by 1/365 again. Since you wind up with really small numbers, it's often easier take the reciprical and say the coincidence would happen once of some number of tries.

For the mixed up birthdays, the first person has 3 possible birthdays out of 365 that would match, the second would have to match one of the 2 remaining birthdays out of 365, and the third would have to match the remaining birthday. Multiply the three probabilities together to get the overall probability. (The easy way would be to use n!/365^n with n being however many birthdays you're trying to match up. n! factorial is every number from 1 to n multiplied together).