Math 326, March 31 - The
Birthday Problem
Suppose you have a room full of people. What is the
probability that two of them share a birthday? The result is
surprising. We begin by computing the probability of two people
sharing a birthday in a room of n
people (following 7.1).
Additional Questions
- Create a simulation where Excel randomly generates 24 birthdays.
Program Excel to check if there are any duplicates. Using a Data
Table, conduct 1000 trials of the simulation. Compute the
percentage of the trials which result in some shared birthdays, and
compare this percentage to the probability we computed earlier.
- A teacher asks her class to write down an integer between 1 and
100 (inclusive). If there are 20 students in the class, what is
the probability that at least two students will have written the same
number? If the teacher wants to be 95% sure that a duplicate will
occur, from how many numbers should she have her students choose?
- If your class is choosing from numbers between 1 and N, how big
can your class be and still have a 95% chance of a duplicate choice? Make a graph which shows the
size of class you can have for N between 1 and 500.