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?