The Monte Hall problem is from the TV show Let’s Make a Deal. Monte, the show’s host, offers you 3 doors to choose from. Behind one of them is a new car. Behind the other 2 doors are goats. You pick one door. Monte then opens one of the other doors to reveal a goat. He knew that door had a goat. Then he gives you the choice to switch doors from your original pick to the remaining door. Should you switch? Does switching give you better odds of winning the new car? Why?

The Conjunction Fallacy was made famous by Amos Tversky & Daniel Kahneman in their work “Judgments of and by Representativeness”. They created an example called The Linda Problem. Here it is from Wikipedia:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

  1. Linda is a bank teller.
  2. Linda is a bank teller and is active in the feminist movement.

Most people pick #2 that she is a bank teller and a feminist. In the telling of this problem more information is often given in order to enhance even further the illusion of you being given more information.

The difference is that in the conjunction fallacy you’re given more information but it’s not relevant to the outcome. Where is in the Monty Hall problem you are given more information and it is directly relevant to the outcome.