First try this experiment. Find out the birthdays of as many members
of your family as possible. Do any of them have their birthdays on the same
**day** of the year?

Now try the same experiment with all the members of your class. We will see how likely it is that two members of a group have the same birthday.

Consider each member of a group, one by one. The first person will have his/her birthday on a particular day.

**Problem 1** What is the probability of the second person having
a different birthday from the first?

**Problem 2** What is the probability of the third person having
a birthday different from the first and second?

**Problem 3** What is the probability that at least two of the
first three people have the same birthday?

This solves the problem for a group of 3 people. As expected, it is not likely that any 2 out of 3 people will have the same birthday.

**Problem 4** Repeat the problem above for 4 people. What
is the probability that at least 2 of them have the same birthday?

**Problem 5** Using either a computer program or a calculator,
solve the problem for a group of *n* people, where *n* = 10, 20,
30, etc.

**Problem 6** What is the probability that 2 members of your class
have the same birthday?

**EXTENSION**

How many people are needed in the group to be 95% sure that there will be at least two with the same birthday?