What Are The Odds?

Here’s a quick exercise you can do to demonstrate why understanding statistics and probability is important.

The Birthday Paradox

1. Consider a Group You Know: ask your students to think about a group of people. This could be a group of Facebook friends or Instagram followers, the fans of a sports team they follow or a group of people at work or school.
2. How Many Shared Birthdays? Ask them to write down approximately how many people they think there would have to be in that group for it to be more likely than not (i.e., more than a fifty-fifty chance), that two members of the group share the same birthday.
3. The Answer: reveal to them that typically, you only need a group of 23 people for there to be more than 50% chance that two of the group members share the same birthday. They’ll probably find this hard to believe.

You should find that most, if not all of your students, will have instinctively thought that you need a much higher number than 23 people in a group for this birthday match to occur.

Known as the birthday paradox or the birthday problem,this seemingly counter-intuitive finding provides psychology instructors with an engaging starting point from which to build an invaluable student learning experience.

Coincidences Happen Often

This activity could be used as part of statistics class, or it could be used to introduce the concept of probability theory. It could also be used as way of helping students think mathematically about randomness, probability and chance.You might also want to encourage students to listen to this excellent and humorous BBC podcast where they discuss the idea of randomness. Start at 15:31 to hear the hosts (and mathematician Alex Bellos) discuss the birthday paradox.

“Most coincidences, if you actually crunch the numbers, become a lot less amazing” – mathematician Alex Bellos

Alternatively, either as an individual or group project, students could be encouraged to test out the birthday paradox themselves. This would simply involve them having to think about a way in which they could access the birth dates of a group of around thirty people in order to see whether any of the dates match.

As a fan of the series, I checked out the cast list of The Walking Dead and discovered that Steven Yeun (Glenn) and Tom Payne (Jesus) both celebrate their birthday on the 21^st of December.

What are the odds? A lot more likely than we think.