General intuition can often seem appropriate, however, situations arise every day, where, if intuition is applied, one may be left feeling like the world is against them. A general understanding of probability can help one understand these everyday situations and change the way you perceive the world around you. TheInspection Paradox states that whenever you "inspect" a process, you are likely to find that things take (or last) longer than their "uninspected" average. (Williams, 2021) Often people will default to the average of a situation, however the average does not always tell the whole story.

Inspecting a process can often find hidden factors that were overlooked during the intuitive approach. These factors can often help us understand a situation beyond its initial layers and help us understand why using the average is inappropriate. The average is appropriate when things are equal. So, if every class in a school has exactly 30 students, the average is appropriate, as every class is equal. Polling a dozen students, your results will be 30 students. However, if class sizes are unequal, the average may not be the best way to figure out the average class size. So, if we were to poll a group of 12 students, and 2 people answered their class size was 10 students, but the other 10 people answered they have 50 students in their class. The average would then seem to be 43 students. However, the average class size may still be 30 students. Inspection of the probability of the situation tells us that for every student that has a class size of 10 students, there are 5 students who will be in a class size of 50 students. The small data set (students polled) gives false results for the average. So, say the school has class sizes of either 10 or 50, and there are equal numbers of each. The overall average class size would then be 30.(Williams, 2021)

Initially, I believed the intuitive approach to be related to subjective probability, but upon closer inspection, intuition seems to be its own approach, without the use of actual probability. The article does help us understand probability however and gives a few examples of how empirical probability may not solve for the correct outcome. In the situation exampled above, a data set of a dozen students gave us the empirical probability of there being 43 students as the average, however, upon closer inspection we learned that there was a 5x higher probability of polling a student from a class of 50 students as there was of polling a student from a class of 10. Understanding this, we can understand how there can be a class size of 30, despite sample test results.

I had never truly considered it in my 39 years on this planet, but probability plays a larger roll in my life than I had thought. In hindsight, there are many instances where I felt the odds were stacked against me for some reason, or that I was having bad luck, but after reading this article, I feel I will have a different view of things. I can now see myself using probability in everyday situations to make better estimates. Understanding that probability can not always be determined by empirical methods still troubles my analytical mindset but knowing that a closer inspection of the data set can reveal the answers is greatly relieving.

References

Williams, L. V. (2021, October 4). When intuition fails, how to use probability and statistics to find the real answers. Phys.org. Retrieved October 27, 2021, from https://phys.org/news/2021-10-intuition-probability-statistics-real.html.

Question 1

Can you think of a past example from your everyday life, where you have felt the odds were against you, however in hindsight of the situation, and an understanding of probability, you now have clarification?