The Concept of Probability, and Puzzles and Paradoxes

Paradoxes and puzzles are vital in the development of probability theory because contradictions and counterintuitive examples are plentiful wherever uncertainty and chance rule. Probability gives rise to paradoxes if the mathematical path contradicts our intuition and in case of resistance to forming new knowledge related to probabilistic notions (Borovcnik & Kapadia, 2014).

Possible events and outcomes are subject to uncertainties, and intuition becomes an essential tool in such a scenario if there is no possible means of using technology to derive an exact number. For this reason, it adopts the principle of contradiction and counterintuitive that contributes to the puzzle and paradox, respectively. In the field of mathematics, statistics and probability have a significant role than other fields. Resistance to form new knowledge is more common in probability than in other subject areas or mathematical disciplines.

The human brain uses shortcuts that work well in some cases but fail in others. The cognitive abilities humans have gained through evolution rely on heuristics and shortcuts to make efficient decisions (“Bias,” n.d.). Such heuristics help make decisions that apply in ancestral environments. In the modern world, there are fewer such situations. More decisions rely on well-informed and technical solutions.

Hence, the chances of relying on impractical heuristics in these scenarios rise. Most decisions made from intuitions can be wrong because humans develop heuristics through which they view the world. It can cause trouble because it picks up the flaws in imaginations and intuitions formed. However, when not surrounded by a technical environment, we tend to rely on our intuitions and judgments that result from a reflex action and gut feelings which we tend to believe more than anything else.

It can result from our background, values, past experiences, or the environment that forms intuition as the weapon to made decisions.

References

Bias. (n.d.). LessWrong. https://www.lesswrong.com/tag/bias

Borovcnik, M., & Kapadia, R. (2014). From puzzles and paradoxes to concepts in probability. Advances in Mathematics Education, 35-73. https://doi.org/10.1007/978-94-007-7155-0_3