Problem Solving

Let me illustrate this using a famous problem-solving task. Try to solve the following problem: The combined cost of a bat and a ball is $1.10. The bat costs $1.00 more than the ball. How much does the ball cost? Before reading on, take a few moments to solve the problem. (No, really. Give it a try.) The answer that immediately springs to most people’s minds is $0.10. But this is incorrect. If the ball cost $0.10 and the bat cost $1.00 more, the total would be $1.20, not $1.10. The correct answer is actually $0.05. Even though solving this problem does not require sophisticated mathematics, more than half of the participants at elite universities and more than 80 percent of participants at less selective universities answered it incorrectly

Source

This is about thinking fast and slow. In tennis thinking fast is OK but in other domains thinking slow is better.

Another Example

Imagine that you can win a prize by selecting a red marble from a bowl that contains both red and white ones, and you can choose whether you’d like to pick from a small bowl or a large one. The small bowl has 10 marbles, one of which is red (a 10 percent chance of winning). The large bowl has one hundred marbles with fewer than ten that are red (a less than 10 percent chance of winning). You know the odds, which are clearly marked on each bowl. So which bowl would you choose? Rather surprisingly, over 80 percent of people chose the large bowl, even though they knew that the odds of winning would be lower. We are evidently compelled to choose this bowl because it contains the larger number of winners.