A certain advertising firm needs to find a recently married couple who are both born on April 19th. They send the intern to the city hall in NYC to look through the records.

- If she looks through 50,000 records, what is the chance that she finds at least one such couple?
- If you were to approximate the above probability with a limit theorem what distribution would you use? Explain why.
- If she relaxes her search criteria to only look for couples with the same birthday, what is the chance she finds at least one such couple after looking through 50,000 records?
- If you were to approximate the above probability with a limit theorem what distribution would you use? Explain why.
- Before starting, the intern is interested in estimating how long this task might take. How many records must she consider to have a 80% chance of finding a couple matching the first search criteria? What about the second search criteria?

In the above, assume that the date people are born is uniform over the year and each person’s birthday is independent of each other person’s birthday. Also, assume that the day one is born does not influence one’s choice of spouse.