## The Birthday Problem...With an Added Evil Bonus

Summary:

I'm horrible with math. Anyone willing to help me out here? (Note, this problem is derived from a comment made in a meeting at work. This is not a homework assignment.)

I want to calculate the probability that two people in a room of 18 people have the same birthday in the same year and were born in the same US state given equal likelihood of any given date being the birthdate and any given (existing) state being the birth state. I say existing, because some of the dates in the calculation include days prior to Hawaii becoming a state, so part of the probability is based on 49 states (all equally likely for that timeframe) and part of it is based on 50 states (also all equally likely from that point forward).

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I get the idea of the birthday problem. Where I get lost is extending that to include the same year and then further the same state. I also don't know answers to questions such as do I account for the days between the oldest and youngest person in the room or the oldest person alive that was born in the US (since everyone in the room was born in the US) to the youngest person in the room? How do you factor in the addition of Hawaii as a new state partway through the possible birthdates/birth states in the equation?

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For what its worth, here's some data that may (or may not) be pertinent:

According to Wikipedia (let's assume this is credible info) Elsie Thompson is the oldest person born in the US that's still living. She was born on April 5, 1899.

Of the 18 people in the room the oldest was born January 20, 1953.

The youngest person in the room was born on Feb 5, 1987.

There are 32,083 days from Elsie's birthday to the birthday of the youngest in the room.

There are 12,435 days from the birthday of the oldest person in the room to the birthday of the youngest person in the room.

There were 49 states in the US until Hawaii became the 50th state on August 21, 1959.

There are 22,052 days from Elsie's birthday to the purchase of Hawaii.

There are 2,404 days from the birthday of the oldest person in the room to the purchase of Hawaii.