Wason Selection Task

One of the most intriguing instances where our brain goes awry is shown in the Wason Selection Task (also known as the Wason 4-Card Task). Before getting too detailed, though, let’s try it. The goal is to solve this puzzle:

If there is an odd number on one side of the card,
then there is a vowel on the opposite side

Which cards do we need to flip over to verify the rule?

Think you have an idea? Upwards of 90% of adults get this puzzle wrong.

The Gambler's Fallacy

At the roulette table, black comes up six times in a row. The gambler thinks, “Since half the time black comes up and half the time red comes up, the wheel is due to land on red,” and bets on red. This is the gambler’s fallacy.

Why is the gambler wrong? Isn’t it true that half the time the wheel will come up black and half the time it will come up red? These are some loaded questions. It is true that given an infinite number of spins of the roulette wheel, red and black will each come up half the time. Even in only a few spins we expect the wheel to come up red and black relatively equally. However, this certainly doesn’t happen every time. At any given point in time, it just as likely to spin a red as it is to spin a black, regardless of how the previous turns came up. That is, the probability function is memoryless.

So why is it that people expect the wheel to ‘even itself out’?

Quantitative Virtual Reality

Theory and practice make for an interesting relationship. The world would be beautiful if all theory came out true in reality. Of course, some things would be difficult to observe in reality. Can you imagine watching in real-time someone shooting a basketball 1,000 times? Or the number of red beetles that drive by? Just simulate it! Seemingly anything of numerical quality can be simulated; this includes basketball shots, options pricing, and the temperatures of the day. This is called a Monte Carlo simulation when a numerical algorithm is run based off repeated sampling of random numbers. 

Base-Rate Neglect

Here’s a probability problem:

At a university, 15% of students are of legal age to drink (21 or older), leaving 85% illegal. There is one liquor store near the campus. Willis, the owner is very good at detecting a fake ID. 90% of the time he correctly stops a student trying to use a fraud license. Unfortunately, Willis isn’t perfect. He also misidentifies proper ID’s 10% of the time. So he has always has an accuracy of 90% when examining students’ identification. Say a student walks in and hands his ID to Willis, and Willis turns it down. What is the likelihood that this student is under age?