The birthday problem. A famous example in probability theory shows that the probability that at least two people in a room have the same birthday is already greater than 1/2 when 23 people are in the room. The probability model is

• The birth date of a randomly chosen person is equally likely to be any of the 365 dates of the year.

• The birth dates of different people in the room are independent.

To simulate birthdays, let each three-digit group in Table A stand for one person’s birth date. That is, 001 is January 1 and 365 is December 31. Ignore leap years and skip groups that don’t represent birth dates. Use line 139 of Table A to simulate birthdays of randomly chosen people until you hit the same date a second time. How many people did you look at to find two with the same birthday?

Chapter 19 Exercises 427 With a computer, you could easily repeat this simulation many times. You could find the probability that at least 2 out of 23 people have the same birthday, or you could find the expected number of people you must question to find two with the same birthday. These problems are a bit tricky to do by math, so they show the power of simulation.