1. If there are 30 people in a classroom, what is the probability that at least two have the same birthday? Compare this to the approximation given by formula (8.1).

2. How many people should there be in a classroom in order to have a 99% chance that at least two have the same birthday? (Hint: Use the approximation to obtain an approximate answer. Then use the product, for various numbers of people, until you find the exact answer.)

3. How many people should there be in a classroom in order to have 100% probability that at least two have the same birthday?

A professor posts the grades for a class using the last four digits of the Social Security number of each student. In a class of 200 students, what is the probability that at least two students have the same four digits?