When probability roams the free world, it tends to trip people up. One of its prime offenses is the conjunction fallacy. Take the problem:
Gregory is a very accomplished man. He graduated from MIT with a PhD in Computer Science in only 2 years, and started his own software company. He is now a multi-millionaire.
Which of these explanations is more likely:(A) Gregory is 19 years old(B) Gregory is 19 years old and a child prodigy
Many people respond that B is a more likely explanation. Let’s try another:
Victoria has spent a lot of time in the hospital. She has undergone 14 surgeries and suffered from 3 heart attacks. She has also been a keynote speaker for the American Heart Association.
Which of these explanations is more likely:(C) Victoria is an avid baseball fan(D) Victoria is an avid baseball fan, but suffers from a congenital heart condition
In this problem, many people choose answer D. The correct answers are A and C. Why, do you ask?
The probability of two events occurring is always less likely or equally as likely as only one of the two events occurring. A probability diagram helps explain this paradox:
If this probability is so straightforward, why do we tend to get the answers wrong? The conjunction fallacy. When the mind attempts to find reasoning for scenarios, it looks for an explanation that seems to be the “best fit”. It would be extraordinary for a boy of age 19 to have multiple degrees for MIT and be a multimillionaire, running his own company, but being a child prodigy better explains that. In the same way, it is not particularly likely that an avid baseball fan has a failing heart and has gone through numerous surgeries, but it makes sense that a woman suffering from a congenital hearth condition does. We look to find a best fit explanation rather than relying on pure probability. The inability to appropriately designate the probabilities of certain events (namely assuming the conjunction of two events be more likely than only one of the events) is known as the conjunction fallacy. We are not wired to observe the world based on pure probabilities, but rather to search for cause and effect to explain phenomena. Yet again, intuition fails to guide our way through logic puzzles.
