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The simple math problem that many people get wrong and what it teaches us

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Why so many are wrong

Το απλo μαθηματικo πρoβλημα πο υ πολλοΙ κανουν λαθος και τι μας μ&alpha ;θαiνει

“A baseball bat and a ball cost a total of $1.10. The bat costs $1 more than the ball. How much does the ball cost?''

Most people find this math problem easy and answer almost mechanically: The ball costs 10 cents. But this answer is incorrect.

If the ball costs 10 cents, then the bat costs $1.10, so the total is $1.20.

The correct answer is that the ball costs 5 cents and the bat costs $1.05.

This question is part of the Cognitive Reflection Test (CRT), which was created in 2005 by psychologist Shane Fredrick. As CNBC explains, Fredrick wanted to see how people resist—or don't resist—their intuitive thinking.

The original test included two more questions.

– If 5 machines it takes 5 minutes to make 5 toys, how long would it take 100 machines to make 100 toys?

– Inside a lake, there is a spot with water lilies. Every day, the area of ​​this point doubles in size. If it takes 48 days for the water lilies to cover the entire pond, how long would it take for them to cover half of the pond?

Studies on whether this test actually measures cognitive ability or intelligence have mixed results.

However, the reason many people give the wrong answer is a psychological trap we sometimes fall into. The same psychological trap can prevent us from making good decisions.

Why So Many Get the Problem Wrong

People think in two distinct ways. Psychologists refer to this cognitive process as System 1 and System 2. System 1 is our initial reaction, which often unfolds quickly and without thought. System 2 is when we use conscious thought and effort. Daniel Kahneman popularized this idea with his book “Thinking, Fast and Slow”.

To activate System 2, we must realize that System 1 did not give the correct answer.

For some people, the intuitive answer is that the ball costs 10 cents. To arrive at the correct answer, they must realize that System 1 did not work and re-examine the problem.

Of course, having a second chance to solve a problem does not automatically mean that one will find the right solution.

Even when given a second chance, many people stick to their original answer, as a recent study showed, in which researchers gave participants 50 versions of the stick and ball problem.

The participants first had to give their answer with System 1, or their initial intuition, and then were allowed to give an answer with System 2, which was supposed to be more careful.

“The results showed that both people's initial intuition and the answers they gave after discussion remained predominantly biased from start to finish,” the study says. “But on the rare occasions that participants learned to self-correct, they were able to immediately apply the solution strategy and provide a correct answer for the problems that followed.”

According to CNBC, this shows that when making decisions, it is important not to always follow our intuition. What one should do is reevaluate their choice, even if their intuition says it was right. What one has to think about is whether they are really analyzing the problem or just looking for the easiest answer.

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Source: www.kathimerini.com.cy

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