The Monty Hall Problem
This puzzle is called the Monty Hall Problem.
You should switch because if you do, you have a 2 in 3 chance of winning. If you don't switch, the probability of winning is 1 in 3.
The intuitive answer for many people is that the probability will be 1 in 2 after the host opens one of the doors. But our intuition misleads us here, as it does in many cases.
Think about it this way: If you initially picked the wrong door, and you switch, you will certainly win. There is a 2 in 3 chance you initially picked the wrong door, so there is a 2 in 3 chance you will win if you switch!
More Puzzles
Courses
Fallacy Detectors
Develop the skills to tackle logical fallacies through a series of 10 science-fiction videos with activities. Recommended for ages 8 and up.
A Statistical Odyssey
Learn about common mistakes in data analysis with an interactive space adventure. Recommended for ages 12 and up.
Logic for Teens
Learn how to make sense of complicated arguments with 14 video lessons and activities. Recommended for ages 13 and up.
Emotional Intelligence
Learn to recognize, understand, and manage your emotions. Designed by child psychologist Ronald Crouch, Ph.D. Recommended for ages 5 and up.
Worksheets
Logical Fallacies Worksheets and Lesson Plans
Teach your grades 3-7 students about ten common logical fallacies with these engaging and easy-to-use lesson plans and worksheets.
Symbolic Logic Worksheets
Worksheets covering the basics of symbolic logic for children ages 12 and up.
Elementary School Worksheets and Lesson Plans
These lesson plans and worksheets teach students in grades 2-5 about superstitions, different perspectives, facts and opinions, the false dilemma fallacy, and probability.
Middle School Worksheets and Lesson Plans
These lesson plans and worksheets teach students in grades 5-8 about false memories, confirmation bias, Occam's razor, the strawman fallacy, and pareidolia.
High School Worksheets and Lesson Plans
These lesson plans and worksheets teach students in grades 8-12 about critical thinking, the appeal to nature fallacy, correlation versus causation, the placebo effect, and weasel words.
Statistical Shenanigans Worksheets and Lesson Plans
These lesson plans and worksheets teach students in grades 9 and up the statistical principles they need to analyze data rationally.