Bayes’ Theorem Applications
http://www.askamathematician.com/2011/10/q-what-is-bayes-rule-and-how-do-i-use-it-in-daily-life/
In this forum, a mathematician discusses the various ways Bayes’ Theorem can be used to properly calculate the chances of some event occurring given some evidence. The author states that people tend to fall victim to the base rate fallacy. An exemplification of this would be if I told you that breathalyzers display false drunkenness 5% of the time, yet they always detect if a person is truly intoxicated. One in a thousand drivers is driving drunk. If the police office stops a driver at random and forces them to take a breathalyzer test which indicates that they are drunk what is the probability that they are actually drunk? One might say a percentage as high as 95; however, the truth is that the answer is 2%. This is because for every 1,000 drivers tested, 1 driver is drunk, which is 100% certain; however, 999 drivers are not drunk, and among these drivers there are 5% positive false results. This means that there are 1 + 49.95 = 50.95 positive test results, which makes the probability 1/50.95 or around 2%.
This is a great example at how we tend to grossly miscalculate probabilities and the importance of evidence. Many times, people tend to incorrectly calculate probabilities under the false assumption that various pieces of evidence hold more significance than they actually do. While many people do not have the mental capacity to run calculations through Bayes’ theorem, one can still use it more abstractly to estimate the probability of an event occurring given previous information and introduced evidence. While in class we used this theorem to calculate information cascades, it can be used to calculate many more events in our daily lives.