Posts Tagged ‘counter-factual’

A very simple problem (which most University level students get wrong).

A bat and a ball cost $1.10 between them.

The bat costs $1 more than the ball.

How much does the ball cost?

It’s not as simple as it first appears.

Most people answer 10¢. We’re betting you did, too.

But the correct answer is 5¢.

Why? Well, if the ball cost 10¢ and the bat cost $1 more, then the bat would cost $1.10, making a total cost $1.10 + $0.10 = $1.20. Wouldn’t it?

This puzzle appears in a book by the behavioural economist Daniel Kahneman called “Thinking, Fast and Slow”.

According to Kahneman, more that 50% of students at the top US universities (Harvard, MIT and Princeton) get this problem wrong. At less prestigious universities the number of students who gave the wrong answer was more than 80%.

Kahneman writes:


The distinctive mark of this easy puzzle is that it evokes an answer that is intuitive, appealing … and wrong.

Do the math, and you will see.

If the ball cost 10¢, then the total cost will be $1.20 (10¢ for the ball and $1.10 for the bat), not $1.10. The correct answer is therefore 5¢. It is safe to assume that the intuitive answer also came to the mind of those who ended up with the correct number — but they somehow managed to resist the intuition.”

The bat-and-ball problem is an observation that is a vital fact: many people are overconfident, and prone to place too much faith in their intuitions. They apparently find cognitive effort at least mildly unpleasant and avoid it as much as possible.

This also explains the enduring appeal of fake news, populist politics, and conspiracy theories.

Too many people believe what they want to believe, or what “feels” right, and ignore critical thinking or facts. So when someone asks you “How can people believe [insert politician’s name, political theory, conspiracy story, or whatever you like in here]?” then it’s probably because they’re relying on intuitive thinking and not logical thinking.

In the most simple terms, most people simply can’t be bothered to think.

Perhaps they don’t know how to, but it’s much more likely they can’t be bothered to employ the effort required.

And the implications for our society are serious, and frightening.